Thanks for all the advice guys!! We do require renters insurance so I will ask her to look in to filing a claim if she wants. I would assume there is a 500-1000$ deductible though so I am not sure how much it will help her. Thanks for that tip @Kim Meredith Hampton and @Steve Babiak. I did not realize renters insurance would pay for that.
The only thing I "promised" her is that we would compensate her so at most I would maybe prorate her rent and take of those days to compensate her. When I told her that I thought it was purely faulty sewer line and not a wade of 8 tampons lol. When she asked about the hotel bill all I did say I send me your receipt and I will look at them but I didn't not say how much I would cover. Our house rules are referred to in the lease, which she signed, and they say expenses from drain stoppage are the tenants expense and also no flushing tampons.
I am leaning towards paying the plumbing bill because of the roots but not paying for her hotel or compensating her. You have a good point Steve but I do not feel I need to compensate her since I was basing this of of incorrect information. Then again maybe giving her a small amount like $100 might help her be more understanding. I might mention she has not been the best tenant but I guess that doesn't matter all that much. She hasn't broken anything in the lease/rules until the tampons.
It seems like most of you guys think that would be appropriate. Thanks so much @Chris Eaker, Steve and everyone else for the advice! We are only about a year into owning rentals and this is our first sewer issue.