Enter Google Voice. It allows you to set up a free...yes, totally FREE...phone number that will forward to your cell phone. You hand out your Google Voice number to parents, which they can text or call like any number. It will forward the messages or calls to your phone , which you would answer like any regular text or call. It works differently (and likely easier and more natively) on android phones; but on the iPhone, texts show up in my messages tab.
Yes, you can stick with giving parents your work number. For many, that may be an easier and more comfortable option. However, I think the extra features you get with something like Google Voice make it worth the small bit of effort!