MySQL too many connections on shared server
max_connections is probably set to 151.  And this is probably because of running a newer version of MySQL.
Assuming BlueHost allows you to change the config file (and they may even have a UI for doing such), change that to, say, 1000.
Having hundreds of 'simultaneous' connections is not, in itself, a &quot;bad&quot; thing.  However, it may be indicative of some other problem.
Do the connections hang on longer than necessary?  Is there some form of 'connection pooling'?  What is the client -- does it have a limit on connections to it?  Are you also having CPU or other performance problems?  How long does one user stay online and connected?