Can bed bugs be transferded to another person?

Probably not. Unless they somehow carried a bed bug with them to work without noticing, and you carried that bed bug home with you without noticing. In addition, it would have to be a pregnant female, that would lay its eggs in your home. Since you can feel a bite within minutes or an hour (it itches like a mosquito bite), you shouldn't be caught off guard. I suppose one could be hiding in their purse, and then jump into your purse, but this seems like a very unlikely situation.