I work full time so I am entitled to the full annual leave entitlement
Legally you are entitled to the same number of hours leave as full time employees, not the same number of days.
My boss asked me to convert it to hours and then back to days, so if I take 4 days leave, I don't go in at all that week, and use 4x9 hour days of leave
That is correct.
The reason that taking 5 days off on a bank holiday week would take up 5x9 hours of leave days is because my boss asked me to covert the leave, including bank holidays, to hours, and then covert it back in to 9 hour days, and use a day of leave for a bank holiday
That is not correct. You should only be taking a day of leave for a bank holiday if it is a day when you should normally be working. That is the law (the Working Time Regulations, to be precise). A bank holiday that falls on a day when you would not work does not come out of your holiday entitlement.
my annual leave entitlement is definitely plus bank holidays. I know some (stingy) employers do it that way, but not where I work
It is not stingy to express holidays as a total including bank holidays. It is actually legally how all holidays work. An employer offering the statutory minimum can either say that you get 20 days holiday plus bank holidays, or that you get 28 days holiday including bank holidays. Both are exactly the same. However, the latter reflects the law more accurately.
If your employer is giving you the same number of days off as normal employees and also giving you all bank holidays they are being extraordinarily generous. If we assume that full time employees get 20 days plus bank holidays (the statutory minimum) that comes to 28 days per year, 4.6 weeks. If you also get 20 days plus bank holidays you are receiving 7 weeks annual holiday, over 50% more than normal employees.
Legally, if normal employees receive 20 days holiday per year plus bank holidays, you should be getting 22.4 days holiday per year including those bank holidays that fall on your normal working days. Bank holidays which fall on days when you would not normally be working do not come out of your entitlement.