Sorry for my ignorance, but how do you ground the parking brake? Which wire to where?
Well, the simplest way to do the bypass is just to tap the ground wire running into the UB10BT itself. Do this by attaching the wire tap at the end of the light green wire to the black wire coming from the U310BT. Tighten the tap with pliers, and you're done. Bypass complete. This is probably what 95% of owners will do.
What I'm suggesting is that you actually run the light green wire to the parking brake, and attach it to the ground wire coming from the brake. The manual instructs you to attach the tap to the "power connector" wire of the ebrake; just attach it to the other wire (ground) and it will be bypassed. The ground wire will probably be black or white with a black stripe, but this varies by vehicle. (Check your manual.) This way, if you get in an accident, there's less likelihood that your bypass will be found (opening you up to a lawsuit), and you can claim that you at least tried to install it correctly in states where operation while bypassed is illegal.
The law varies by state; I posted a list below. Most state laws only pertain to video screens in the driver's line of sight, and in this respect the U310BT may be less of a legal problem to bypass. However, even if a bypass is legal in your state today, the law may change, you may move, or you may be pulled over in another state. Legal or not, none of this will protect you from a frivolous lawsuit claiming you were "distracted" during an accident. Wiring to the parking brake ground rather than the ground from the unit itself may offer some protection in that regard.
I am not a lawyer; this is not legal advice, just my opinion. Whichever way you decide to go, let us know if you have any problems and we can try to help.
AVIC-U310BT Installation Manual
http://www.pioneerelectronics.com/StaticFiles/Manuals/Navigation/AVIC-U310BT_InstallationManual0526.pdf
US State Vehicle Electronics Laws
http://www.digitaltips.org/in-vehicle/stateLaws.asp
EDIT: I don't know what laws are applicable in Europe, Canada, etc. I live in Florida, where my amateur reading of the law is that a bypass is perfectly legal, since the U310 doesn't display video and the law "does not prohibit the use of an electronic display used in conjunction with a vehicle navigation system."