I've been told to do something about my hair by an employer
Doesn't sound like they're asking a whole lot from you so that's awesome.
Don't get an "alice" band. They're a pain in the ass. I wore them a lot as a little girl and they just give you headaches and slide off your head.
Get "elastic" head bands. They look like regular hair ties but they're HUGE in comparison. They usually come in multi packs of rainbow colours or neutrals. I use them all the time to either keep hair off my face or just to tie back my dreads since regular hair ties can't even get around them once!
Get the ones fully encased in fabric though, not the wide, flat ones where you can see the elastic woven into them. The flat ones hold well but the elastic snaps a lot in my experience.
these guys are what I'm talking about. If you have a hair and beauty section in your supermarket they should be there.