Strategically, Biden has a difficult choice. As Republicans (and Russians, btw -- link below) play up Biden's supposed cognitive decline, people will look more to his VP choice.
The Republicans would probably rather attack that choice politically, but if she's a moderate then they will launch veiled attacks against her gender and race. Also, if she's moderate, Biden has less chance of exciting his base that's already not too excited. Lastly, if she's moderate, then it will mean that Biden is playing the same game as Hillary and focusing too much on the center at the expense of progressives. As Hillary moderated in hopes of a big victory, enthusiasm and support for her decreased so much that Trump was able to squeak by with 80,000 well placed votes.
I think Biden needs someone progressive to draw a stark contrast to Trump's radicalism. That way, the more the Republicans create the illusion of Biden's decline, the more younger people will be motivated to vote, and Biden will more than likely hold onto those more moderate who know that he is far more cognitively healthy than Trump. Karen Bass, because she looks presidential, is head of the Congressional Black Caucus, and the baggage against her so far is pretty trivial, seems like a very good choice. And she'd match up well against Pence in a debate.
Since some of the posts bring up her comments on Scientology in 2010, here’s a google news search for “scientology” from 2000-2010. So, she really is right when she says we didn’t really know as much about Scientology back then:
Also, has far as the right accusing her of being a communist or a socialist, I really think red-baiting only appeals to the over-70 set, and besides here’s a nice link to comments by Trump:
Trump: "I was really tough and so was he, and we went back and forth," Trump told an adoring crowd of thousands at Wesbanco Arena in Wheeling. "And then we fell in love, OK? No, really, he wrote me beautiful letters, and they’re great letters. We fell in love.”