3 possible solutions for you....
Just fill the tub with a little water and then use a plunger over top of the drain. This is the least messy and most effective way.
From a wire hanger, clip off the straight bottom piece (where a pair of pants would hang) using a pair of pliers or wire cutters. If you only have a pair of pliers you can bend the metal until it snaps where you want it to break.
On one end,fashion a T handle big enough to hold onto.
On the other end,bend a little hook about a quarter of an inch wide. You want it just wide enough to grab onto the gunk but not big enough to get stuck in the drain.
Fish the hook end down into the drain and start feeling around. You don't need to go very far since most of the hair and goo get tangled in the drain mechanism.
Most drains have a plus-sign shaped drain with four holes around it. Use the tool carefully in each hole and try to hook onto the hair clumps and pull them out. It may take a little practice, but you will soon get the hang of it.
If you feel like the tool is stuck on something just push it back in and twist it until it comes out easily.
Keep doing this until you don't feel any more hair or obstructions in the drain.
Put the hair in the trash.
Turn on the faucet, test the drain and rinse out the sink. You should find it draining just like new.
My parents and some other people I know used concentrated bleach, and it did wonders. However, if you are worried about the ecology aspect of it, not a good one.