Is there a remote desktop app for iPad that works well with a bluetooth keyboard?
Screens is probably the best app for that. Works with OS X builtin screen sharing but can connect to all VNC sources. It has a really smart way of translating touch to mouse events but also has bluetooth keyboard support, including modifier keys. And tons of other features. It runs 2560x1440 sessions smoothly on my side, you can pinch-zoom to get the scale you like.