A day visit to Cockscomb is worthwhile, but, yes, it's better to stay at least overnight. You'll have a better chance of seeing wildlife. You'd probably want to stay (camp or cabin) at the Cockscomb visitor centre.
Yes, you can do it by bus, although you'll have to walk or hitch or pay for a ride the 6 or 7 miles into the preserve from Maya Centre.
You'd be better off going at least overnight to Ian Anderson's. Busing up and back you wouldn't have much time to do anything. You can camp there for not a lot of money, or get a cheap dorm bed.