You could try using draino
Had this problem. Removed drain cover. Pulled out a ten year accumulation of hair. Could not believe amount of hair. Drano would not have helped my problem. Drain worked fine after this. Be prepared to be grossed out.
Does your bathtub have a special, 'anti-clog' drainage for 'long' hair.'? The easiest thing I h ave foubd
If it's not hair, try pouring about a cup of baking soda down the drain, followed by about 1/2 cup of vinegar. Let that sit about 20 mins that rinse through with hot (not boiling) water. If it's better, but not quite free flowing yet, repeat. Wishing you the best.
Usually its hair, I have a drain snake I got at the Dollar Store and some paper towels. I take the drain cap off but you can do it with it on too. Stick it down there and pull back up and wipe off with the towel, repeat a few times, run hot water and see if its clear. Repeat as necessary.