I think what GunsNGears is saying is that, if the problem is that the fuel pump isn't being turned on by the ignition, eliminate the fuel pump. There's a great step by step article to show you how to do it
here. The Suzuki part you need should run you around $40-50. I was going to do it, but the Suzuki dealer where I'm at was going to charge me almost $100 (lovely Canadian dealers).
Gleaning what I have from others on this site, I would try this first to see if it's related to your pump. You stated that your bike runs for about 45 secs and then shuts off. I would try reconnecting your fuel line directly from the petcock to the
carb. Now, you won't get enough flow to actually ride the bike, but you should be able to at least TEST to see if you can keep the bike idling. If the bike keeps idling, then you have narrowed the scope of the problem down to fuel delivery.
Then, it's just up to you whether you choose to go pumpless or replace the ignition. I would check around with some other guys on the site about going pumpless though. It seems some have had great success and others haven't. Hope that helps some!