How are you testing whether Minify is working or not? I’m assuming you are referring to WP Minify?
I am hosted with BlueHost and use this plugin as well and I tried testing it with the plugin uninstalled, and installed. My javascript, according to https://websiteoptimization.com/services/analyze/ went from 30K to 110K … It makes a fairly big difference and is working noticeably on my sites.
If this is the same plugin you are using, I wonder if other plugins might be causing it to work improperly. You may want to try disabling all other plugins and then re-enabling WP Minify and see if it makes a difference.