Hey,
Firstly, welcome to Susan's!

You're not coming off badly at all, you're coming off like a caring person who just wants the best for their SO.
I knew for a pretty long time that my girlfriend was trans, but only because she told me. I'd never really considered it beforehand.
I think, in things like this.. there isn't all that much that you, personally, can do. If she's still figuring out things for herself, or if she isn't even aware yet.. that's her journey she has to make. I know that you, of course, want to know, because it affects you. But she might not be trans, or she might be trans without being aware of it, or she might be aware of it without knowing what to do about it, or she might be aware of it and hate herself for it due to how she was raised.. it's hard for anyone on the outside to tell you what's going on in her head, especially since we don't know her.
But what you can do is just let her know, if it comes up in conversation, that you have no problems with transpeople. And if it's the truth, you could even throw out something like "Hell, if you were trans, I'd still love you the same and want to be with you." Just so she knows she never has to be afraid of telling you.

Or if she's wearing men's clothing and you think she looks good that day, you could be like "wow that shirt looks great on you" or something, to show her you're okay with her clothing choices. Just little things to make her feel comfortable and safe to be herself.

Or, you could always ask questions. I don't know how she would respond to this, it depends on the person, but if she's open to rhetorical questions and stuff you could ask her things like "have you ever wanted to be a guy?" But again, that really depends on the kind of person she is and if she would be comfortable answering.