We've painted over tiles using the proper tile paint.
Looked very cheap and ended up having to retile
Suggest you strongly consider retiling as I'm sure that if you want your bathroom to look nice you will be very disappointed
We have painted tiles at work tha last 4 yrs and not peeling yet, so the most important thing is preparation, I think they use white spirit to clean the tiles, it will tell you on the tin what to do anyway.
It can looks okay depending on colour and your layout. If the money is the issue then this would be cheapest way of doing it.
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