Using a P-channel MOSFET as an on/off switch
As Ignacio is trying to say, you need to pull the gate of the FET up to the 350V supply rail to turn it off. This makes the VGS ~= 0V. Which means the FET is off. 

To turn it on, you need to reduce the voltage on this gate, perhaps the full 350V is not healthy for it. Perhaps drop the voltage at the gate to +330V to turn it on. This will make the VGS = -20V which is plenty. But always check datasheets.

This is a very high voltage switching circuit and your BJT will need to sustain the 350V as well, like I said. I suggest an opto-coupler to isolate the signal from the 350V supply.