This is a bit more on Cu based alloys reference the previous posting on red brass. I am by no means an expert on this topic and most of my experience is from industrial applications, some from gun & accouterment work.
Annealing bronze is a bit unique and as with anything else, the process depends upon the exact alloy parameters you're dealing with. If you raise the temperature too-high, bronze and many other Cu base alloys will undergo changes in the molecular bonding and crystalline structure which negates the desired softening effect of annealing.
The correct annealing temperature for common bronze alloys is between 750°F and 1250°F, this is where you need to either know the exact alloy you're working with or spend a lot of time on trial, error and cull. Heating by "color" is nearly impossible for someone who hasn't had a lot of experience using temperature monitoring equipment and doesn't do it on a daily basis. "Dull red" or "medium red" can each encompass a temperature range that is far wider than the alloy will allow for so the use of exact temperature indicating/reading devices is a must.
The next problem is 'how to heat'. The main purpose of adding P (Phosphorous) is to displace O2 from the melt in order to increase strength of the alloy. The byproduct of deoxidation is phosphorus pentoxide that is removed from the melt during the refining process. In some cases, Fe is added to combine with some of the dissolved P in the Cu forming iron phosphide; in turn, this provides an additional nuclei upon which the grains can grow in the recrystallization process thus creating a finer grain structure. Heating the alloy to anneal it becomes an issue in that to prevent the recombination of O2 into the alloy, heating should be done only in an atmospherically controlled inert gas furnace. Since few of us have these the secondary option is to use indirect furnace heating with the part(s) contained in atmospheric tempering silica; third and least appealing option is using a carburizing or "soft" oxy-fuel torch flame running a very rich fuel mixture so as to reduce O2 contact with the alloy. If all you have is an LPG or MAPP & air torch, there is a way to create a fuel-rich flame but for safety concerns I choose to avoid that discussion.
Fe, Mn, Al and other elements are also added to bronze alloys to give them specific properties; each elements and combinations thereof also create vast differences in the required temperatures of both heating, cooling and rate of cooling for annealing purposes. Also, the length of cooking time and specific temperature directly affects the resultant properties of every alloy the drawing process.
Brass, being a Cu-base alloy, also maintains much of the same "particulars" as does bronze wherein the properties are directly affected by temperature, length of hold and rate of change.
Here's some micrographs to show the differences in the resultant structure of common 70 Cu; 30 Zn alloy at 200um resolution.
As-Cast: Note the cored dendrites showing the unequal distribution of the Cu & Zn.
Cold Worked: Cold working can increase the alloy's strength by >38% but at the same time reduce its ductility by >75%.
Cold Worked & Annealed @ 575°F to recrystallize the grain creating a balance between the strength and elongation properties.
The amount of time and specific temperature at which the alloy is held can also greatly affect the manner in which the grain structure is formed provided the correct rate of cooling and cooling end-point from the hold-point is maintained. I know it seems like I'm beating the "alloy" thing to death but it is imperative to know the exact alloy you're trying to work with since even small variation in the processing parameters can have a marked affect on the resultant properties of the work.
For example, something as simple as a trigger guard or buttplate can cause you a lot of grief. Even if everything goes perfect in the shop, you anneal and work the part as needed without issue then six months later the customer is calling to gripe because it broke for no apparent reason. Yes, it's rare but it does happen and there are two main causes being a poor-quality casting and/or improperly processing the part post-casting. To understand this, we're working with "ornamental castings" and most foundries treat them as such. Bronze type alloys afford a lot more "fudge factor" in the casting process where a "visually acceptable" part may be produced that is completely unacceptable from a metallurgical standpoint. It's not specifically that the foundry intentionally makes crappy parts but normally ornamental castings are not spec'ed for alloy and metallurgical parameters and the primary reason for that is cost. Depending on the specifications, that $15 buttplate could be costing you a whole lot more if you start treating it as "critical" instead of "ornamental"; thus is why you can buy a 1# Cu alloy cast figurine for $20 while a 1# certified Cu alloy cast gear can cost you in excess of $200. This is what leaves you trying to calculate the correct fudge factor in order to obtain the desired results. Most serious issues can be averted as I explained above in trying to keep O2 out of the annealing process, staying below the critical change temperatures and post-work heat treating the part(s). In most cases the fudge factor will suffice but at some point you're going to get that customer service call... Two things that will help you avert problems are a good non-contact thermometer or temperature indicating markers and a simple wet-bulb thermometer for your quench bath. Keeping the quench bath temperature around 90°F ± 5°F will help prevent shocking of the Cu alloys but finding the correct "heat-to" temperature prior to quenching will likely take some experimentation but in my experience, staying within 900-1100°F range is a good starting point, maybe not perfect but often times it's "close enough". If you cold work a piece, re-anneal then post-treat at 550-650°F for 30-90 minutes (requires experimentation) and stay within a cooling rate of 150°F/hr; best accomplished with an electric furnace where you can drop the pyrometer setting at timed intervals. Avoid heat-sinks! Forget about holding or handling the work piece with pliers or tongs, that's the quickest way to create problems for yourself. If furnace heating, use removable tray so as to avoid touching the work completely while heating and on its way to the quench. If you don't have a furnace, suspend the work with the least amount of contact area possible with a thin, strong wire that will hold-up to the high temperature such as piece of 0.035-0.045" Mig wire which also works well if you're heating in an atmospheric tempering silica or similar granulated containment (this is the method I use now that I no longer have an inert gas furnace).
I have used a combination of casting & hot forging Mn & Al bronze gear alloys into daggers & swords but obtaining the proper balance between ductility and strength is not easy and a hundred hours of work can easily lost with one impact test. Gun parts are much less of a hassle but if you're working on parts that aren't "generic", I'd take the time to research the source of the parts and attempt to obtain as much information on the particular alloy they are made from so as to process it as correctly as possible; a few hours spent on the phone can save you a whole lot of hours trying to make a replacement part. Hot forging Cu base alloys can be very challenging and nearly impossible on items with a thin cross-section because the heat loss is too rapid to allow for working time beyond a few seconds. Another problem with hot forging is that no matter how well you clean your tools and anvil the work surface is going to get impregnated with crud; this doesn't make it impossible to accomplish but if the finished items is not to have that "rustic" look, you need to finish out the forging with enough excess material remaining so as to allow mechanical removal of the contaminants.
