Hello. My name is***** can assist you with your question.
You can bypass the timer, but you must have the RJ-22 bypass plug. The good news is that they are pretty much universal and inexpensive. You can get one on eBay for about $9. Here is a link to one:
You're question related to bypassing the timer with the plug - and that is the correct plug to do that - it should work. If it doesn't, then there is something else wrong with the bed.