There's no such thing as a "bike specific" one man tent.
If you're under 6ft my six moon designs lunar solo is excellent but it's hard to find and expensive.
As it's September and it won't be that bad in weather (lets hope) why not take an even lighter option and take a Tarp, you don't need a pole if you rig it up to your bike.
The best on the market at the moment is the Mountain Laurel Designs Trailstar which needs a pole
But if you are working to a budget don't forget a cheap tent will have a poor hydrostatic level, so I would chose a better quality tarp like these from Alpkit
https://www.alpkit.com/products/rig