iOS devices can only print directly to AirPrint printers.
All AirPrint printers are wireless, Bluetooth is wireless, but not all wireless printers are capable of using AirPrint. Your HP OfficeJet 100 printer is not an AirPrint printer.
To print directly from an iPad / iPhone you will need an AirPrint compatible printer or another device to act as a print server. That can be a Mac computer running Printopia ($19.95 with free trial) or handyPrint (donation - supported). The Mac must be "on" but may be asleep for them to work. Equivalent PC options may exist but you're on your own finding them.
You can also buy this standalone print server:
These options enable you to use any printer available to your Mac, even older ones that may predate AirPrint by decades.
Otherwise you will need to buy an AirPrint printer or multifunction device.