Going by fluff and the game stats of some units, eg. Avalon class cruiser and Merchant-class JumpShip, then ASFs can operate from Small Craft bays. The same would also apply to Conventional Fighters & Fixed-Wing Support Vehicles operating from DropShips and large Support Vehicles.
However, judging by the Small Craft Bay entry on the Transport Bay table on p239, the Capacity lists only "1 Small Craft (up to 200 tons)" rather than "1 Aircraft/Fighter/Small Craft (up to 200 tons)", which apparently contradicts the fluff.