I run Moodle 1.9 up through 2.7 on Bluehost shared servers. However, I don't recommend a shared server for production systems. I use them only for testing and development purposes. The main problems are limitations on database connections and server processing power.
My first advice is use a Moodle Partner. If that is too expensive, use some other hosting company that is familiar with Moodle. In the end, host it yourself.
And... if you do not use a Moodle Partner, make a contribution to the Moodle Trust Fund.