Maybe. Buying her a new seat does not make the offense go away, but it may induce her not to follow through with charges. The charges, if they are filed, are most likely to be for criminal mischief in the municipal court where you live. Depending on your criminal history, penalties could include probation, fines, community service, jail and buying a new seat. You would be wise to hire an attorney to reach out to her on your behalf. While this may be more expensive than just buying a new seat, speaking with her on your own and replacing the seat could be seen as an admission of guilt in court, whereas having a lawyer to do this would not be an admission. This is important because arguing that the bike was abandoned may be a viable defense to the charge if it is filed. Call me for a free consultation.
She might decide not to pursue the charges if you buy her a new seat, but as pointed out above you would then be admitting to guilt. Also, just because she no longer pursues the case doesn't mean the DA will drop it automatically. The defense of abandonment is solid in many situations and if you can secure an attorney you might be able to push for a dismissal of the charges as the damage was minimal.
I read your question as indicating you are 15 years old. If that is so this answer applies. You don’t get sued for vandalism but charge with mischief. The case will be heard in juvenile court or for something this small may be referred to a conference committee in your town. The bad news is your parents are going to find out because they get served with the complaint since you are underage. In the past on a charge like this restitution may make a lot of this go away. Talk it over with your parents. Good Luck.