TechManual, 6th printing, page 209, "Bay Door" entry under "Game Rules" states:
The launch rate for any transport bays carrying fighters, Small Craft, BattleMechs, battle armor or ProtoMechs is equal to two such units from the bay per functioning bay door (per turn).
There is also a related statement on
TechManual, page 196:
A transport DropShip’s launch rate (per turn) for onboard fighters or other launch-capable units (fighters, Small Craft, ’Mechs and ProtoMechs) is equal to twice the number of functioning bay doors associated with the launch-capable units. For example, a DropShip with 18 fighters in a single bay that has 2 doors assigned to it may launch 4 of these 18 fighters per turn (2 doors x 2 fighters per door per turn = 4 fighters per turn). Meanwhile, a DropShip that has 12 ’Mechs across two bays, each of which has 2 doors, would be able to drop 8 ’Mechs per turn (2 doors per bay x 2 bays x 2 ’Mechs per door per turn = 8 ’Mechs per turn). Rules for dropping ’Mechs are in Strategic Operations, page 20.
Equivalent passages to the above are also found in
Tactical Operations - Advanced Units and Equipment, page 72 and page 84 and
Strategic Operations - Advanced Aerospace Rules, page 143 while describing construction rules for advanced support vehicles and advanced aerospace units, respectively. All are likely templated from the TechManual passage, as the wording is identical other than the types of units mentioned as examples.
These statements seem to conflict with multiple other references to units launching or dismounting from bay doors in various other rulebooks, and need clarification and/or errata. The "dismounting" rules found in Total Warfare might plausibly refer to a different type of unloading, but the passages in question explicitly reference the dropping rules from Strategic Operations, yet still disagree with them.
Specific references:
Total Warfare, page 86, "Launching" subheading - this is the closest match, stating that two fighters or small craft can launch from each fighter/small craft door per turn with no risk. However, it does not mention the other unit types included in the TM entries, and furthermore allows for
more than two launches per turn as long as each launching unit makes an increasingly difficult Control Roll as the number of simultaneous launches increases. It is also the only other passage to actually use the "launch" wording rather than "dismount" or "drop".
Total Warfare, page 91, "Dismounting" subheading - this entry indicates that 1 unit can dismount per door per turn, not the 2 mentioned in TM (although the "dismounting" wording is technically distinct from "launch rate"). It is also specific to mechs, protomechs, and vehicles, and requires doors of the appropriate types.
Total Warfare, page 207, "Dismounting" subheading - once again indicates a maximum of 1 unit per door per turn.
Strategic Operations, page 20, subheading "Atmospheric Drops" -
this is the biggest conflict, as it was explicitly referenced in the unit construction passages, but it states that "A carrying aerospace unit can drop a number of units each turn equal to its operational door capacity", i.e. the usual 1 unit per door per turn, not the 2/turn stated in TechManual or TO/SO advanced unit construction rules. Space drops for orbital insertion or ground units in zero-G operations reference this subheading and therefore follow the same limit.