I have done three 3 week tours across Oregon camping as we went.
We carried a light weight back-packing tent for 2, light weight sleeping bags, a tarp, a very light weight backpacking stove, one change of clothes, rain gear... etc., etc.
We did stay in a motel one night during an electrical storm and frequently ate "out" to lighten our food load. (Carried breakfast, snacks, and 1 or 2 freeze dried dinners.
We put panniers on our bikes which handled the loads pretty well. The weight made climbing over McKenzie Pass, Willamette Pass, Santiam Pass, and the Crater lake area difficult and slow, but the beauty made it totally worth doing.
Sounds like your camping trip will be short, so you can probably get away with less gear and it could be heavier. You might not want to buy new gear until you know if you like bike camping.
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