There isn't a bus from Bodrum to Dalaman airport. You will have to go into Dalaman itself and then I think you will be able to get the Havas bus to the airport, but I don't know the times sorry.
Yep, Dreamgirls is a drag act - you can have a meal and then watch the show, or just watch the show.
As for trips - boat trip (book the Topol Kamil at the Hotel Baba on the beach for a great chilling day), jeep safari (good fun), village tour (nice half day out into the hills), trip to Turgetreis or Milas market (or you can do this on your own by dolmus), a trip into Bodrum to sightsee and shop. You can also get around the peninsula by dolmus and see the other resorts - Yalikavak, Bitez, Gundogan, Gumusluk and Golturkbuku (very upmarket) are all great to look around.
Bars - on the beach Roy's Place which is always popular, on Bar Street there's Central Bar (very popular later on and banging music), on Adnan Menderes Caddesi you've got Leo's, Chico's, Smileys, Cheers (my local LOL), Radio Bar (great for watching sport if you're into that). Of course, there's probably new ones that will open when the season starts but those I have named are good. Oh and at the top end of Adnan Menderes Caddesi there's Mr Frogs (if you're into karaoke), Outback Bar (Indie-type music if you're into that).
As for Bodrum, there's loads of bars to choose from - the White House is always popular as is Kule .. and if you want to splash out, there's Halikarnas and Club Catamaran.