The contact no for the Bristol Flyer (airport bus) is +44 (0)870 580 8080, for details of times, etc.
Trains go at 8:41, arr 8:51,
8:46 arr 9:03
9:00 arr 9:08
So quite tight, really.
There's later trains to Dorchester at 9:32 or 9:55 but they involve 2 changes and take 3 1/2 hours. Or 11:19 is a direct train.
What time do you have to be in Dorchester?
This site seems to think that you can get to Dorchester from Temple Meads direct if you take the Weymouth train on First Great Western trains. It leaves at 9:49 which gives you more leeway. I just searched Bristol Airport to Dorchester, arriving by 12pm.
HTH