Hi Monica, sounds like you have high traffic site. Whats your current host?
There are always alternatives. Bluehost has been acquired by Endurance International not too long ago that are known for cutting cost and sacrifice customer experience quality. We were seeing good reviews and now they ar not that great for BlueHost: https://webhostinggeeks.com/user-reviews/bluehost/
In order to advise you better I need to understand if you need to move onto VPS or Shared host is enough. Maybe a shared host with high availability (like webhostinghub has) will do the job.
Which CMS are you going to use?