[R52], [R53], and [R54] all would ban bluetooth communication between the cRio and a secondary device during competition.
As for modding the cRio to accept bluetooth, I do not know if it is possible. But i would just suggest if at a demo you would like to use a secondary computer on the robot to monitor or communicate, the cRio has external RJ-45 ethernet ports available all ready.
R55 also explicitly denies the use of bluetooth communication during competition at all.
You need the Driver Station computer running to enable the robot. If you are talking about how you talk to the cRIO with a second computer, I’m looking into the Network Tables stuff used by the Smart Dashboard. Looking through the SmartDashboard stuff on the robot and dashboard sides it looks like the Dashboard is just a Network Table with a specific name and you should be able to just make a new table with whatever name you want (or possibly just use the SmartDashboard table? I’m not sure yet if it would work with 3 devices).