however this causes a need to connect my 12v ground to the ground of the other supply, is this a bad design?
No it is quite normal and it is required for your system to work, not only with the measurements but also with the control:-http://www.thebox.myzen.co.uk/Tutorial/Power_Supplies.html
should I perhaps filter the connection between ground with like an lc circuit?
No definitely not. That would cause the two grounds to be at different voltage levels. This is known as ground bounce and can cause problems even when the grounds are connected directly together.
Is there a proper way to connect to two grounds?
It is called a star connection, all the grounds meet at one point, so in your case the two power supply grounds, the H-bridge ground and the arduino ground should all be at one physical point. That is not chained one to the other.
a way where I wouldn't have too?
This is caled isolation, it would require opto isolators for the arduino into the controls of the H-bridge and some form of galvanic isolation of the input voltage to the arduino. One way to do this is with an opto isolator with two photo transistors, one goes to the analogue input and the other acts as a feed back to an op amp on the H-bridge side, this is so you get a linear transfer.