Can I use a single wire as the BT Antenna?
could just use a single wire as the antenna?


Sure, that's called a monopole antenna. You'll have to make sure it's the right length and that you offer enough of a ground plane. Also, impedance matching is a thing, since the feedpoint impedance of a monopole usually isn't what you can use in a transmission line on a PCB.


  I have seen wifi devices with a single wire soldered or connected to the board with a short run of the wire being used as the antenna.


I doubt that. The things you've probably seen are small-diameter coax cables leading to a dipole, since that works better without a defined ground plane.

Sure, a random wire works better than no wire at all, but chip antennas are smaller and cheaper to assemble than wires, and would usually work at least as well.