Not sure if this is the right forum...

The bassist in my band has recently been developing pain in the hand between her thumb, and first finger of her Strumming hand. After shows it sometimes becomes inflammed, etc. She's been playing guitar for years, and this is a recent thing..

Just wondering if anyone else has come across this specific pain in their hand, and have found a way to remedy it, or know what it is(tendonitis, carpal tunnel, etc.)

Probably carpal tunnel. Have her get it checked out pronto.
Studies have shown that 92% of guitar players are close-minded. Copy this into your signature if you're part of the 8% who enjoy rap.
Does it have a numb feeling.
It could also be damaged nerves.I have that in my leg.

Best thing to do is just go to a doctor and have it checked.
Nobody here is going to be able to help you. Visiting a doctor will. Tell him/her to go visit a doctor. Don't put things this important in the hands of a bunch of unqualified people on UG.
He who joyfully marches to music in rank and file has already earned my contempt.
He has been given a large brain by mistake, since for him the spinal cord would fully suffice.

Remember: A prudent question is one half of wisdom.