Personal training position - should I even bother?

I've begun applying to a few places this last week. I walked into a small gym the other day (actually while in my workout clothes after leaving my own gym) and asked if they were hiring. The guy behind the desk asked what position I was asking for, said that they were not hiring front desk when I mentioned, but then told me they were looking for personal trainers. I had been thinking of becoming a personal trainer to help me through college (just not so soon).

I told him I wasn't certified and he told me that they would certify me. I asked how long it would take and he said only about 2 weekends (workshops). He gave me the application and left me his phone number (said he was the general manager) and the manager's phone number. He also somewhat introduced me to two of the guy trainers who were standing in the background ("That's Scotty, and that's Matt...they're both pretty goofy but fun to work with") He told me that they "really" needed female trainers.

I really would love the job. But I don't have work experience and I don't have real references. I'm really doubting I will get the job...but I know I should at least try. There are two professors I could ask to use as a reference - My Nutrition professor and my Human Biology professor. I figure they're well related. I don't know these professors incredibly well. I've only had 4-5 classes so far with the Nutrition professor. I do ask a good number of questions(usually responds with great question!) and I sit near the front. I received an A on the first test this last week. However, I came in late for that test and was almost not able to take it. And I didn't manage to turn in an assignment - a dietary log. I do well enough in my Human Biology course as well...the professor is somewhat of a pushover I could say...she wants students to like her and to find her cool. It's a larger class, I don't ask questions (nobody does really), but she seems to recognize me. I'm afraid to ask these professors, especially because they don't know me entirely well and it may be awkward if they didn't want to or something...but they're really all I have. My other references are way too old (and I was told this during an interview a while ago)

I don't have work experience and I don't have strong references. I am not certified (though they would certify me...I'm not sure how ready I would be anyway. I need to learn more exercises) I've been going to the gym (a larger one) 4-5 times a week. I have a nice body; apparently I look like a personal trainer. Anyways, should I even bother? Am I likely to get the position?