If it's not a boot leak, it's most likely a carb problem, probably lean. Here's the order that I would check things:
1. Fuel tank vent line(s) plugged
2. Check the coasting enricher diaphagms first- they are easy to get to-- don't lose the tiny seals! My money would be on these being deteriorated.
3. It's not likely, but you may have a stuck choke (also easy to check)
4. You could have a sticky float- check the float levels with the engine running to see if they oscillate. Use a clear tubes on the bottom carb drains, looped up to the coasting enricher fastener head as described in Clymer's. You would have noticed a petcock or fuel flow issue at higher speeds. Write down the measurements, in case you need to adjust the level later (it may come to that.)
5. You can do this stuff with the carbs still on the bike: You can try Seafoam fed into the bowls by the vent line and letting it soak for several hours before draining- open the drains to let the fuel out first. You may need to clean the carb pilots mechanically (with a pipe cleaner and solvent by opening up the drain cover.) There are also little holes near the throttle plate on the I.D. of the intake- spray carb cleaner in there. Remove the idle mix screws and spray carb cleaner in there, too (don't lose the o-ring and washer!)
6. If all of the preceeding fails, you probably need to take the carbs off and go through them. If you are mechanically inclined, you can do it yourself. I usually gingerly use an impact screwdriver to remove fasteners, even on carbs. Otherwise, you will be trying to slot the heads with a dremel after you strip the heads. And when that doesn't work, you'll have to drill them out.