What to do if paint peeling on bathroom walls?
...what is causing it?

There is a very high probability that the person who applied it did not sand the gloss off of the existing paint prior to applying the new paint (bathroom paint, typically, has a gloss to it).

Do I need to apply any anti-bacterial compound before painting again... ?

No

Do I need to apply any special primer?

Not if you prepare it properly, meaning sand off all unsound paint that is peeling or seems like it might peel, and ensuring all surfaces below the peeled-off paint are also de-glossed. Make sure the wall is smooth, dull, and clean and you can repaint.
Notes-

if you paint over existing unsound paint, it will all peel again eventually
if you patch (or sand through to bare plaster) you will need to prime
if you choose to use a high quality bonding primer (after proper surface preparation) it will do nothing but help.