Thanks for the specifics
If I walked into a session cold with that set-up, I'd put a DI on the output of the bass, especially for catching low B on the 5 string, and a large diaphragm condenser about 3' in front of
the 4x10. Using the DI before the amp makes a big difference, as most built-ins use opamps to drive the balanced output and can't compete sonically with a basic Jensen transformer based DI. If you don't have one, get thee over to Jensen's site, download the schematic, and order the DB-E tranny. It's a quick job to put together, I use $5 ammo boxes from the surplus store down the street for a durable case. The Alembic probably has enough gain to go straight into a comp and then to tape, using the make-up gain to set the level, so I'd listen to that sound on some tunes as well.
Miking amps with tweeters is never fun, they tend to beam and limit your placement options. That's why I'd start with a condenser, you can pull it back to get a blend of the speakers and tweeter without losing as much bottom as a dynamic would. One of my studio cabs is a SWR Goliath II and I disconnected the crossover and tweeter 10 years ago, sits in the mix much nicer for me that way. Otherwise, seems like you've got the approach down, bring up the mic and DI, have her play the piece you want to get down, then blend 'em, change positions, swap mics and in general F with it until it sounds right for the song being played. You might find it easier after you've done a take and she can play along with the other instruments while you change the tone, then you can really find the perfect fit. Might just be a 57 pointed at the neck and all this other stuff is balderdash! HTH
Oh, and don't forget, if nothing's working real well, try changing the bass part, sometimes playing with an odd tone can give birth to the coolest ideas.