Good Route For Crossing Bangkok

[eastbaybob]

I'm going to ride my bicycle across Bangkok and on to Chachoengsao on a Sunday morning at the end of May. I am going to start off on the west side of the river in Nonthaburi, crossing the brige that is on the 302.

From there does anyone have an idea for a route that would be relatively quite for Bangkok?

And while I'm at it, are there ferries that cross the river down towards its mouth? Near where the ancint city is?

Thanks

EBB