The last time I got into a fender bender was a couple of years ago.
When I got into the fender bender which was my fault it only raised my auto insurance cost up to $5.00 per month more.
But it took at least a year before they raised my auto insurance rates and then a year later my auto insurance rates went back down.
So there's not much need to worry about your auto insurance going up too much as long as you keep a pretty good driving record.
If the fender bender was not your fault then your auto insurance costs should not go up.