You can't go around BKK (yet) south of the city. To avoid (too much) traffic I suggest generally 4 to Nakhon Pathom, 323 to Kanchanaburi, 324 to Suphan Buri, 329/33 to Nakhon Nayok, 33 to Pratchinburi, 3077? through Khao Yai Nat park etc.
You can find all the small roads on your own map to avoid the main roads and to be able to relax and take in where you are rather than concentrate on everyone else. . Ie 3394 from Ban Pong to 3356 to 3260 to Suphan Buri etc....
Hwy 9 (ring road) would be quicker but....