I’ve had to have a plumber come and clean out the bathtub drain three times in the last five years. I’m quite careful and added an extra screen on the drain so that hair doesn’t go down.
I was away for three months and so the bathtub was not used in that time. When I got back, it seemed to be backing up again.
Do I need to call the plumber again? Is there anything I can put down the drain to help clear it?
Could there be some deeper problem?

It all depends on what the plumber found when the drains were cleared previously.
Was it hair causing the clog/
How far in was the clog?

it cant hurt to try

Unfortunately, I really don’t know how deep it was, but I think the last time he was here he definitely went deeper.
I’m guessing I need to call the plumber.

You can buy a 25-foot snake cheap at Mallwart or any hardware store. If it's further than 25 feet then your other drains would be clogging too. There are hair clog removers that are about 20 inches long for a few dollars. They may be worth a try. I don't have hair anymore so I can't test them.