Does anyone know if you can catch the same bus that takes you to Krabi town from the airport back to the airport?

Catch the Shuttle Bus from Ao Nang across street from Chok Dee Restaurant at around 8.30am, 10.30, 1300, 2pm,, 4pm, 5, 5.30, and 6.30pm. 90 baht. Bus company phone 085-8892664, times can change. Good Luck

The OP is in Krabi Town, not Ao Nang.

I remember a few years back hopping on a songtaew on Utarakit Rd. in town which was near the waterfront / Kong Ka Pier area, where a lot of the guesthouses are clustered. It connected with Phet Kasem Rd. which dropped me off at the airport. About 100 baht then, but now it might be more. Ask your guesthouse or hotel manager where the nearest stop is for this particular songtaew shuttle.

Alternatively, you could just wait for the official shuttle bus to show up where it dropped you off in town, assuming you took it there from the airport initially.

For others wanting more information, here is a fairly recent photo (08/2009) taken at Krabi airport which shows the shuttle prices to various locations:

Good luck.