Mosfet behaving differently with other power supply and same voltage
You need a commmon ground between the two. Probably your bench supply (-) output is grounded and the other ones are not, and you are getting a ground through the USB cable and your PC, so the grounds are connected through the 3-pin wall plug when you use the bench supply. If you unplug the PC it will probably stop working. You may wish to use a 1K resistor between the two grounds, just in case. 

Also (and this is not the cause of your proximate problem), your BUZ11 is really an inappropriate part for that service. It's not a logic-level MOSFET and is only guaranteed to fully turn on with 10V Vgs. You should use a MOSFET that has an acceptable specified Rds(on) with 3.3V or lower Vgs. The particular sample of BUZ11 you happen to have may sort of turn on enough typically, but that is not good engineering at all.