I will let my B partner do the first 2 or 3 BLS runs, and then I will offer to alternate with them. My old partner would always refuse, and take everything BLS, with the exception of babies. He just didn't like those runs. However, I can't stand mental/emotional runs, so the trade off was that he knew I would never offer to take one of those.
I just got a new partner, so we are working out the details of how things are going to go, long term. So far, we have mostly had BLS stuff, and he has taken everything. Just like my previous partner, he feels that there are plenty of days where everything is ALS, and he can't tech anything, so he doesn't mind the days we get hammered with BLS stuff. Like someone else already said, it all evens out over time.
We both check out the truck every shift, and whoever did the driving to the ED is the one that restocks the truck when we get back to station, if it is a run-of-the-mill type run. That's because the tech still has additional computer reports that have to be done on the station computer. If it's a big run where lots of stuff has been used, everyone helps restock.
We also take turns driving. One shift, I will do all the driving, with the exception of ALS transports. The next shift, my partner will do all the driving, with the exception of BLS transports.