NO ONE actually stocks very many OEM parts, especially for our ancient machines. NO ONE.
And sadly, us ordinary mortals cannot order from the Suzuki mothership directly.
All the online OEM parts sellers are dealers that then order the parts from Suzuki's warehouses, then ship to you. So expect two or three business days before the dealer gets the parts, maybe an extra business day for separating individual orders and repackaging, then whatever additional time it takes for shipping to you.
My preferred parts purveyor is a local dealer that happens to have an online parts sales website. I order my goodies, then when they call (And they do actually reliably call me when my stuff shows up! Stellar service!) I take a pleasant 20 minute ride to pick up my goodies and slobber on some new bikes and suchlike. They usually get parts in two to three days, so I can shortcut a few days of packing and shipping and skip paying shipping costs by choosing "will call". And prices are nearly identical to any other online parts shoppe.
This site belongs to Westfield Power Sports, just north of Indianapolis. It's where I order all my goodies, and they ship nationwide. Great people.
https://www.onlinecycleparts.com/
If you poke around locally, you might just find a dealer with a similar mutually beneficial arrangement.
Caveat A: if you walk into the dealer or call, expect much higher parts prices. Ordering online gets you a discount because you don't have to wake up the parts monkeys and force them to interpret your mouth noises and turn them into part numbers.
Caveat B: There are a few large reliable fleaBay sellers who appear to have stocks of NOS parts, probably inventory purchased from defunct dealers, or dealers clearing out old stuff. These can be great sources for OEM parts at a discount. For example, the more expensive gaskets like head gaskets or valve cover gaskets are often available this way and can save you a fair bit of cash. Look up the part numbers and see what you find on fleaBay. If the part number has been superceded, try the old and new numbers. Sometimes this works, sometimes not, but it's worth looking.
For example, a head gasket for my GS850G, 11100-45121, is $95.69 at OCP, and these pop up on fleaBay for less fairly often (about $80 right now, but I've scored much better discounts many times). That said, you do have to beware, and make sure you're getting an actual OEM part; a lot of scammers are peddling low-rent imitation Chinese crap using the Suzuki part number. You'll start seeing the same few sellers pop up.
For smaller items, like clutch cover gaskets, seals, o-rings, fasteners etc. it's often not worth the effort to track these down on fleaBay unless you're bored enough to work on your stockpile over the winter.
Another thing to watch for on fleaBay is old parts stashed in the new packaging and sold as NOS. This isn't always a deliberate scam; some people have the absolutely baffling, inexplicable habit of placing the old broken part carefully in the new part's box and then placing it on a shelf. Thirty years later, their heirs clean out the garage, and you can guess the rest. ALWAYS make sure you get good pics that give you a good look at the part and look for oil, opened bags, etc. You expect some rattiness on dusty NOS parts, so it can be difficult to tell the difference from a couple of blurry cell phone shots in the dark. I've gambled and lost a few times.