Does it help you to practice conversations that are causing you anticipatory anxiety? If so, practice what you'd like to say and how you'd like to say it.

I used to have trouble being assertive, but then I started working on a job that required me to be that way. I finally started to feel much more comfortable being that way in my personal interactions, too. First off, you have to accept that one can be assertive without being confrontational. Assuming you're the former and not the latter (unless the situation warrants it, you're good to go). Second, you have to accept that even polite assertiveness is going to rub some people the wrong way AND that that's not your problem. Trust your ability to handle yourself appropriately. If somebody reacts badly to that, then too bad. It's out of your control.

Here's the simple truth that you shouldn't overthink: Your bike isn't working properly even after a tune up. Call them up and tell them that and ask if you could schedule an appointment to have it looked at again. They probably won't even bat and eye, especially if once they get it in the shop, they can see what you're talking about. But, again, don't overthink it.

As for you more generalized LBS anxiety: I've found that it helps if I do my own background research before going into a shop so that I have some baseline of knowledge. It's helped me feel more confident and make better buying decisions, and it quickly dispels whatever stereotypes they may have about female riders/new riders. There are lots of resources on the web; you just have to be willing to invest the time. But understand, too, that some shops and some shop employees just aren't that great. I hope for your benefit that the new shop is a good one, but if you end up getting a bad vibe no matter how you approach them, it might be them, not you.