What your work is saying is that your total holiday entitlement is 112 hours a year, but you don't get bank holidays on top of that. As a part timer you are entitled to the exact same holiday entitlment as a full timer, including bank holidays, but all in proportion to your hours. So if full timers are entitled to 8 paid bank holidays, then someone working, say, 3 days a week would get 5 of those, if that makes sense.
Your work are saying that if you want to take bank holidays off, it comes out of the 112 hours total, it's not given on top. What the arrangements are for if you want to work the time I don't know, that's a company thing. If you work the time you will keep your holiday for another time.
The crucial thing is to make sure that you are getting the same entitlement as a full timer on a pro rata basis. Do you know what the full time holiday entitlement is where you are?