Last year we drove from Hua Hin to Pattaya for the Burapha bike week and we crossed the river via the ferry at Prah Pradaeng.
This might be an option from Pattaya.....? Once you cross the ferry make for Samut Sakhon then head North West. You will avoid most of Bangkok (tollways not allowed in Thailand for bikes) following this route.
Maps below where we crossed.
Regards,
GN.
Edit: not sure how to upload pics.....
Google Maps location: 13.658101,100.53477
Is there a better way than going via the expressway across the Chao Praya river from pattaya to kanchanburi without going into bangkok? Is there still a car ferry at samut prakan?