Before changing a server to combat bandwidth overage issues, see if adding a CDN solves your problem. Its usually a quick and cheap fix.
One of our client sites was on an old server and getting hit with a lot of traffic due to some recent publicity and marketing. The traffic was not expected to die down soon. A new website was in the works but could not be launched till the website was completed in full. It was a large site with a lot of functionality. The host was sending bandwidth overage bills that needed to be fixed quickly. The solution was to add a CDN. In this case StackPath. By doing so the load of serving static files was shifted to the CDN’s infrastructure and there was an immediate drop in traffic to the old server. Using a CDN may be a fix for others in the same situation and it comes with added benefits such as faster performance, lower latency and SEO advantages due to the speed improvements.