If it's that bad, you could always just shave your head. I'm being serious here - it's very freeing and generally looks much better than you'd think.
Otherwise, wash your hair but do not condition it the night before (so it's dry when starting your ride). Once you get to work, dry it off with a towel to the extent that you can. Then brush it with a boar's bristle hairbrush. This will help distribute any sweat and oil in your hair throughout all of it, such that it should just look and feel nice and soft. I've done this before and it works pretty well for me. There are also a number of hairstyles you could try that eliminate visibility of a large part of your hair; I like wearing a bandanna and pulling back the rest of it.
You could also borrow one of the doggy hair-dryers and use that!