So far so good.

A tarp is a good idea.

Don't forget a pad to put your sleeping bag on. I forgo a pillow in favor of a stuff sack with clothes I don't have on that I use for a pillow at night. You'll need the extra clothes if you get wet. Be sure to have a waterproof bag or garbage bag to keep extras dry along with a towel.

I have a smallish tube of environmentally friendly soap that I can use to wash myself, my cook stuff and brush my teeth. What you use might be dictated by factors like whether or not you are in bear country -- in that case, you need to be scent free in your choice.

I make due with a spork, a small stove with fuel and swedish firesteel to light the stove (it's light and small and works when wet). My lightweight cookset is a pot and a bowl. I splurge and bring a metal camp coffee mug but could make due with just the bowl.

Don't forget bike tools for the bike and spares of things like a tire and tubes with patches/glue. I also have a light weight backpacker's multi-tool in addition to the bike specific multi-tool.

You'll need lights for your bike and for camp. Some use a flashlight mounted to handlebars that can be removed, though I have a bike light that I remove and use as a flashlight.