Too bad there's no good documentation of how airline pricing works that I could reference... (or is there? maybe somebody has already said all of this in the FlyerTalk wiki somewhere?). Let me digress back to basics for a minute.
To fly on an airplane you need two things: A reservation (identified by a passenger name record, or PNR), and a ticket (identified by a ticket number).
The reservation is an entry in one or more airlines' computers (and maybe also in a GDS) that tells each airline to expect a particular person (or group of people) to show up for some flights. Reservations have passenger info, a list of flight segments, and a booking code for each segment indicating which inventory you have reserved. To create the reservation, there has to be enough inventory available in the requested booking codes for all of the passengers on the PNR (ignoring things like waitlists and standby).
A ticket is some sheets of paper, and/or more commonly these days some records in a (probably different) airline computer, that serves as proof that you've paid for some travel. A ticket is good for travel for one person on a sequence of flights. Multiple passengers traveling together will each have their own ticket, though they may be on the same PNR. A ticket consists of a series of "coupons" (even an electronic ticket has virtual coupons), one for each flight segment. Each coupon also refers to the booking code that is paid for on each segment, and there is a fare calculation that shows which particular fares are used to arrive at the final price.
It is possible to have either thing (the reservation or the ticket) without having the other thing, but you can't usually travel without both. The inventory on the ticket and the inventory in the PNR have to match. The ticket and reservation can also refer to each other (though they don't have to). Up until recently you could still write out tickets by hand. I'm not sure if anyone still allows this. It's also sometimes possible to "split-ticket" and pay for each passenger on a single PNR with multiple tickets.
There are rules that determine how fares get combined to make up your ticket, and how various fees, taxes, and surcharges are added in. Each fare on its own also has rules. In addition, there are general principles for fare construction (spelled out by IATA for international travel), and each airline may have exceptions to the rules (spelled out in their own published rules).
To finally get back to the point at hand, there is a complex chain of logic that determines whether a fare can use a particular booking code. Here are some things that go into the calculation:
- the "prime booking code" filed on the fare (usually, but not always, the same as the first letter of the fare basis code, YUP fares booking in A are a common exception)
- a "booking code exception table" which may be part of the fare rules and tells what to do under various situations (e.g. telling what an F fare will do on a plane with no first class cabin), or for international travel, telling what booking codes to use on other airlines
- international fare construction principles, like "mixed-class differentials" and "higher fare entitlement" may allow you to book in a different cabin than the fare is for
- finally, there may be some airline-specific logic that each GDS implements for each airline
To answer the original question, the "/f bc=A" trick on our website is used to restrict the fare (or fares, it doesn't limit the number) used to pay for that portion of travel to fares that have a prime booking code of "A". From everything I've said above, you can see that that may or may not control which booking codes are actually used for each flight segment. But it usually will. And a change of booking code may or may not cause a breakpoint between fares to appear.