I can believe that drilling a jet is not the best way, but it is a technique that used to be very common, at least back when cars had carburetors.
The first thing you need to do is get a set of drill bits that will do the job, and something to hold/turn the bit. Forget the number on the jet, find the largest drill bit that will fit into the jet now and then go up one or two sizes.
Note that you can only go larger and there is no going back so unless you have a pile of too small jets then you would probably be better off finding new jets. If you found new jets instead of drilling out your old ones you can always go back, which you might need to do later if you change altitude or make some other change to the bike.
I just went through a re-jetting exercise on my bike which also has a Mikuni carburetor. I had the opposite problem, I needed to go a lot leaner than the jets available from OEM dealers would get me. I contacted JD Jetting and although they didn't have anything for my bike they pointed me in the right direction and I finally found a website that sold jets. Lots and lots of jets.
Try looking at
www.cyclewearables.com Do a site search on Mikuni. I bet that they have what you need, probably about $5 each. You will be able to buy a range of jets for less money than a set of drill bits that you would need.
Warning: their website sucks, their communication is terrible, and they take their time shipping but I did get the jets I wanted.
Rod