I have not tried an Apple to USB adapter, which can be found on Amazon for around $12. You would still need to have the printer plugged into a wall outlet to power the printer.  Now I have tried a compatible Square printer that can connect the USB printer to a Network Router or a WiFi repeater with a USB port and when your Ipad is connected to that WiFi you can print a receipt or other things from Square to it.  I have done this with my printer from an Android cell phone for testing purposes.  This also works if the printer is connected via 10/100/1000 ethernet cable.

The easiest way to do this would be to have a bluetooth printer close to your Ipad, and no cables to connect and disconnect when moving the Ipad around. When connected via BlueTooth you can only print from One Square device though.  I tried my receipt printer to both my Ipad Stands via bluetooth, and it would not work.  So I connected the printer back to the network and now it prints from both Ipads and from my Cell if I need it.

This is the printer we use : mc-print3-receipt-printer 

I chose this one because it connected the most ways at the time I bought it, USB, Network and Bluetooth.  For my application I liked the ability to connect multiple Square devices to it through the Network or as a Shared USB device from my WiFI Extender ( Square sees the printer as a Network Device in this application)