Asking Professor for teaching assistantship I am an undergraduate student and have taken a course which interests me a lot details won't matter I guess).  

The course is split into lectures and lab sessions. The lab prof had a graduate student as a teaching assistant, who simply sat next to the professor doing nothing for the whole semester the course was held (for free it looks like).

Being very interested in the course, I read many textbooks, constantly asked prof questions, answer fellow classmates' questions on the course's forum(which amazed my professor). Finally, I met her in the campus after the course grades were released. She revealed that my coursework was the best in the class and showed my enthusiasm for the subject (150 pages long with complete bibliography list and references). 

Being highly interested in the subject, I am interested in helping my professor during the lab hours, during the final year of my studies.

I have helped other students when I was taking the course, excelled in it, and my professor acknowledged my dedication.

As with any requests made to professors, I am highly worried how to express my will for being a teaching assistant to the course (having in mind that I am an undergrad) without seeming like the arrogant student trying to "replace" the teacher as a result of (falsely showing) she was not doing her work right.

(Stuff that come to mind I'd have to do during the course are - preparation of lab lecture notes, helping students - software problems during lab sessions, help/guidance on the forum, coursework grading, and extra lab sessions.)
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!