I don't know much about the bouldering down here but I think your options are limited to The Agglestone (apparently one of 25 things to do in Dorset before you die, which says more about Dorset...), Lulworth, and bits on Portland.
Some of the sport climbing is good by UK standards, worth bringing a harness for. I've come to really enjoy the trad. down here. It's not Pembroke but there are some excellent adventures to be had. I don't partake myself, but DWS the one facet of Dorset climbing I wouldn't be embarrassed to introduce to a visitor from, say, Boulder or Munich. This is where it all started.
Swanage is about 1-1.5 hour, depending on which bit of the forest you're in, Lulworth or Portland slightly longer. Traffic around Bournemouth could be carnage at the wrong time on a sunny day though.