The biggest thing I would suggest is getting a mic on a nice tube amp to go along with the DI sound. Most engineers will spend hours on a snare sound and then plug you into a DI, say "We've got signal" and consider that a bass tone. Luckily, most basses sound pretty decent under those circumstances- it's just a cool sounding instrument- but you can get so much more with just a little extra work. Just talk the engineer into micing up a bass amp- if you can find an Ampeg B15 you'll be 90% there- maybe get a little bit of grit on the amp and find a nice mix between that and the attack of the DI. Matter of fact, I say don't worry about leakage (most of the best records have tons of it) and play live with your drummer like you're doing a show.
Also, make sure that your bass is properly intonated. Some people are really into changing strings for a session, though taht always sounds too bright to me (but I hate high end in my bass tone, so taht's my hangup). Make sure you don't have any weird shielding or grounding issues that are going to get magnified in the studio.
Good luck, have fun.
