Baking Soda and Vinegar works great to dissolve hair in a drain and I've used this method successfully before for getting rid of hair that is clogging a drain.
To use Baking Soda and Vinegar to dissolve hair in your drain take 1/2 cup of baking soda and pour it down the drain and then take a 1/2 cup of white vinegar and pour the vinegar down the drain and then cover the drain with a cloth or plastic lid.
Leave the cloth or lid on the drain for 30 minutes to let the Vinegar and Baking soda work to break down the hair in the drain.
After 30 minutes have passed you can remove the cloth or lid off the drain and then pour some boiling hot water down the drain and it should be cleared.
If you have standing water in the sink or tub that the hair is clogging you can use a wet/dry vac to suck the water out of the sink or tub so you can pour the vinegar and baking soda down the drain.