is BB (4 Stars) good for non Avenger Battle?

She's okay. BB's skills work really well, which is one of her best perks. The only thing that brings her down is her abysmally low attack stat. It's not that she can't fight against non-avengers but that a servant with class advantage will generally perform better.

Someone like Jalter works because her attack stat is so damn high that she doesn't need class advantage. This is not true of BB so even grailed, she's going to underperform compared to servants of equal rarity who have class advantage.

I think she is pretty good in a tough boss fight if you build a art critical team for her, even non-class advantage. But besides, not quite outstanding. (she also rely on critical star generator, so either have Hans Merlin ready, or put 4060 on)

Yes, she's good and she feels at home the most when you can provide her a good Art team ( be flexible, always adapt, there are lots of available Art teams that can help you ).

There's no wrong in that when we're using our favorite servants all the time, respect to you !
Don't forget to make your own story when you're using her. No need to see things as a dead set here, you can switch between ''gameplay team'' and ''waifu team'', pretty simple. Because like i've been mentioned before, be flexible and adapt.

Bonus :
btw, i can't press the like button for OP for now. Oh sorry it's not there LOL.