My ac was working and then just stopped.

Might be a cam sensor going. If the transmission shifts hard take a look at the sensors. we have a 2007 Chevrolet that had a similar issue.

Why would you want to bypass the compressor? Do you mean to bypass the shut off switch? If the system is low on refrigerant you can bypass the switch by removing the plug and jumping it with a paper clip. Running the system when it is low on R134A would mean it is also low on oil. I recommend adding a oil and refrigerant charge.

I would check the low pressure switch next. The switch cuts power to the compressor if the pressure is too low. The switch can fail.
Same goes for the high pressure safety switch.
As for leaving the relay bypassed, you would need to use a test light or meter to see if you are using battery power with the key off. I would not recommend it.

Low gas can cause this.

ITS THE SWITCH! New Ac Control switch worked out great for my 02 Stratus.. $150 on rockauto.

You need more freon. untill the compressor quits cylcing off so much. the gauges on the diy kits are'nt the best in the world

must check the ac relay and fuses before jumping to the climate control, due to lack of information don't just take it to any body, recommend specialist on AC only

Is your AC on (AC compressor activated)? Try switching that off and see if it still runs.

You need to try reseting the control head. You need to push and hold the the upper and lower buttons on the left side of the control head untill all of the lights start flashing. It will cylce through a flashing lights sequence and then everything should be working fine.

do you mean is coming on and off constalnlty? or works whenever it wan'ts to? if it is cylcing on and off taht means is low in freon or refrigerant