Your doubts about this new friend (probably unfounded) will inevitably show through to a sensitive person and this will only put her off - do you feel close enough yet to actually broach the subject with her - she may be a bit bewildered herself, or feel threatened in the same way as you do (the diffidence and self-doubt could be something else you have in common).
And if it does turn out unfavourably in the end, so what - that's life I'm afraid, and as glib a cliché as it is, it's a fact that there are plenty of other fish in the sea.
Good luck, hope all turns out fine.