The 16-channel Sainsmart board I know has an onboard 5volt buck converter.
Current draw when all relays are on, plus Arduino, plus BT module could be about 700mA.
An inline (with the + wire) 2Amp slow blow fuse will do.
The buck converter will have an idle current.
Educated guess is ~50mA for the Arduino and BT module.
That could ofcourse drain a car battery over time (more than a week).
Leo..