I've only had my Bullet for couple weeks so I really can't comment on problems specific to the RE. But, four cycle engines all being similar in the basic respects, there are a few things you could start with.
It needs spark, compression and fuel to run. All are fairly easy to identify.
First, I would unscrew the spark plug, secure the lead back onto the end of the plug, lay the plug on the cylinder head and kick the engine over with the ignition switch on. It the plug sparks brightly and every other time the engine turns over - this is not the problem. If the spark is weak, only occasional, or not there at all, you will need to troubleshoot through the ignition system.
With the spark plug back in the head of the engine, can you feel a definite resistance when kicking the engine over? A resistance that goes away when you engage the compression release? If the answer is Yes, you should have enough compression for the engine to run. If you have access to a compression gauge, see how many psi your engine produces on its compression stroke. If it's over 100, you should be able to make it run.
Checking fuel. Is there good fuel in the tank? (yeah, I know, but many of us make the assumption only to find out we were low on fuel) Is the fuel tap turned on? Does fuel flow through the tap? Does fuel flow through the fuel line and filter if you have one to the carb? Is there a good amount of fuel in the float chamber? If not the float valve could be stuck in the 'off' position. If fuel in a good amount is present in the float chamber - the carb may still be the problem in that the jets and passageways may need to be cleaned.
I suggest you do these basic checks to see if in fact you have spark, compression and fuel at the engine. I'm sure there are many here who can help you with other specifics to RE I may have not included. Also, it would be very helpful for us to know the results of these basic checks.
Keep the faith, I'm sure it will be running again very soon.
Fred