Yes you can use regular paper and write out a bill of sale by hand without needing to go to the DMV to get a bill of sale document.
Although it looks much better if you do go get a bill of sale document from the DMV and then fill the bill of sale out and then sign it.
For the bill of sale to be a legal binding document the seller and buyer must sign the bill of sale before the DMV will accept it for transfer of title and ownership of the vehicle you're selling or buying.
Whenever I've sold a vehicle and needed to write out a bill of sale I would just go to the DMV and get a bill of sale document and then fill it out.
It was much easier than just writing out a bill of sale by hand and it didn't cost me anything to get the bill of sale document.