Asking Professor for teaching assistantship
There is no reason not to ask. This is all upside for you. You'll show enthusiasm, get a great letter, make an ally. You may not get it, though, for 2 reasons. 

First, as mentioned in the comments, TAships are regarded as part of the graduate training process, and so are awarded to grad students first, often as part of their stipend requirements. It also offers grad students important training in classroom maintenance and teaching. 

Second, from the university's perspective, having an undergraduate take responsibility for a class with undergraduates is a risk, even though you probably are worthy.  Paying students would probably feel slighted to have a peer weigh in on their grade, but that's all speculation. In any case, you are obviously a strong candidate for graduate school. Go for it!