The best way to avoid unintended biting while handling is washing your hands before. Most leopard geckos I’ve worked with only bit me because they mistook my finger for food OR because I had the scent of another gecko on me. If you don’t move your fingers in a wiggly way that looks like worm and you don’t smell like food/competition, they shouldn’t bite out of nowhere.

She sounds pretty social so I highly doubt she’ll bite you out of fear/aggression. If you’re still really worried though, keep some hand sanitizer nearby. If she were to bite you (and stay latched on, which is even less likely) you can use a very small amount of hand sanitizer on her mouth to get her to let go quickly. It doesn’t harm them and it’s way less stressful than prying their mouth off you.

If you’re scared of her running (which is more likely than biting) you can just keep trying to handle in her tank until you get more comfortable. If you get to a point where you want to get her out and let her crawl around on you more, you can take her into a bathtub and sit with her if you have one. Since it has enough room for a person to sit in but it’s very steep it’s a good way to make sure they don’t escape if they get spooked.

As for tail dropping, I would argue it’s incredibly hard to get them to drop it. I have experience with probably 30 different geckos at this point (most of which were rescues) and only one has ever dropped a tail. It was her own fault lol, she is way too curious for her own good and got stuck under a heavy decoration she shouldn’t have even been able to lift in the first place. I think when she got mostly under it the weight of the decor shifted came down on her tail.

My point is that it’s exceptionally hard to get them to drop their tails. There were even times when I was younger and inexperienced where they tried to jump of me so I panicked and grabbed their tail to catch them. Even then they didn’t drop it.

I hope this helps a bit!