Now you never really state that you like her or what you want. So I am assuming you do like her and want something to happen.

I don't know how it would help to plainly say you think she can trust you.

Maybe you need to ask some yes-no question, force her to say no to you. If that works, you shouldn't definitely give up, even if for somet reason it is obvious she isn't truthful.

Another thing you might be able to do is convey to her that you don't mind she is awkward and nervous. You have to do this in a way not to brand her as akward or nervous. I guess it is hard to do, as it both has to be obvious to her, but you don't want to label her.

All shy people who got into relationships always told me they were really nervous at some point, until they realized the other person also was nervous, and that helped lower the nerves. Assuming two people already like each other, I guess it never matters if you are awkward or nervous together, as then it is considered cute. On the other hand, I can see that if you have doubts about the other person and you see nervousness, that can be offputting.

You seem to be measuring yourself using her as a measuring stick. And she might be really odd and thus bad for your ego. If it is all that difficult, maybe it isn't worth it.