If a bath is slow to empty, it's possible that grease or hair have accumulated in the waste pipe, or that something like a hair grip is blocking it.
Pull hair up from the plughole with a bent piece of wire.
lf the bath is still slow to empty, wait for the water to drain and then pour in a solution of washing soda (or borax) and boiling water.
As a last resort, use caustic soda or a chemical cleaner. First let the water drain and then smear petroleum jelly over the metal rim of the plughole to protect it. Pour the cleaner into the hole, following the manufacturer's instructions on the packaging.
If. the bath won't drain at all, place a sink plunger over the plughole and pump it sharply a few times.
There are many fancy plungers on the market at the moment.
Even the most expensive of these plungers is a fraction of what it would cost to call out a plumber so it is well worth you having a go. You will find your local plumbing store stocks all of these.