Similarly, I've only bought parts for a Honda lately, and I've used a variety of sources.
For online, I used Motosports, Bike Bandit, and Partzilla. Partzilla is the one I've stuck with, as they seem to have the most stock on hand and have a fairly accurate inventory tracking system showing lead times. They use a weird shipping system that is tracked through UPS, but actually uses the USPS for the shipping. So far, it's worked, but I keep waiting for the UPS rip-off bill in the form of brokerage fees.
One thing to note that I discovered is that dealerships don't always seem to use the same mark-up. The first dealership I dealt with had pricing consistently higher than Partzilla, but I've since switched to Burlington Cycle, and the pricing is in line with the online sellers once I account for exchange. Some items are slightly cheaper, some slightly more expensive, but it's only by a few percentage points.
The advantage to staying local (aside from supporting local jobs and businesses) is delivery costs and time. I placed an order on a Saturday recently, and had the parts by Tuesday morning with no shipping costs. The only caveat to this is Honda Canada uses a different parts inventory to Honda US, so if it's out of stock here, they have to get it from Japan. If Honda US does have the part, it's much faster to get it online from there. I recently ordered an idle adjustment cable, and Honda Canada said late April for delivery. Partzilla had it packed and on its way in about 4 days, as advertised.
I can't promise any of this applies for Suzuki, though...