Yeah this girl definitely has more on her mind that personal training.
When trainers are of similar age its not completely uncommon to become friendly with them. I had a trainer (granted he was a guy like me) who was a similar age, and we got a long quite well. So sometimes we would text each other random stuff, like about concerts we knew we both wanted to go to, or girls we thought were hot or something. He even mentioned hanging out a few times, but it never happened.
Point is, It's not uncommon for people to form personal relationships in situations like this, that normally you would think should be purely business. However, I will say this, in a situation such as yours, your Boyfriend should take the appropriate action, either tell her to back off if it becomes to aggressive, or simply not play along. Don't text her back all the time about personal issues, or keep the conversations short and impersonal. He also shouldn't accept the football tickets (easier said than done). My sister went after her personal trainer (who was actually a friend of mine) and he told her straight out that he didn't want to jeopardize his job and that he just wasn't interested in pursuing anything.
You're mature in that your not accusing him of cheating, obviously he only has so much control over their actions. What matters is that he isn't reciprocating. If it starts to get really bad, just let him know that you trust him, know he's not cheating, but that it makes you uncomfortable and would prefer if he could tone down the personal contact with these girls, or at least he make it known to them that he is taken and not interested in anything more than friendship. You just have to be careful that you don't make it sound like he can't be friends with girls, which technically is not against the rules, its just when it crosses that line that it becomes wrong, in which case, he's close to it since some of these girls clearly want to be more than just friends.