I don't agree that PT workers get all 8 bank holidays, in my experience it is pro rated based either on the hours or days worked.
As the OP works the same number of hours each day calculating in hours or days will get to the same result.
Using hours, if the FT week is 40 hours then FT holiday is 5.6*40 hours = 224 hours. The OP works 20 hours so is entitled to half as much holiday as a FT worker, 224/2= 112 hours. Since the OP works 5 hours in each of her working days 112/5 = 22.4. This includes bank holidays, so any bank holidays falling on work days must be taken out of that allowance.
If we calculate using days, a 5 day a week worker (assuming the same number of hours each day) gets 5.65 days = 28 days. The OP works 4 days so is entitled to 28/54 = 22.4 days.
Assuming you were there at the start of the year and your leave year runs jan to Dec then there are the following bank holidays:
1 Jan Tues
29 March Fri
1 April Mon
6 May Mon
27 May Mon
26 Aug Mon
25 Dec Wed
26 Dec Thurs
7 of the 8 bank holidays fall on your working days so you need to take 7 days off your 22.4 days, leaving 15.4 days if holiday excluding bank holidays. This will vary each year depending on how the bank holidays fall in relation to your day off. I am not certain whether this is a new job and whether you started it after the beginning of your employer's leave year.