There are no direct trains between Wuzhen and Suzhou and buses are the most convenient ways to get between these cities
There are two daily bus routes that serve Wuzhen from Suzhou:
Departures from Suzhou Railway Station Northern Square Bus Station (苏州北广场汽车客运站), located here, just north west of the main train station. You can get here by taking the subway line 2 (red line) or line 4 (blue line) to Suzhou Railway Station (苏州火车站) and exit from the main door of the railway station. This bus costs 36RMB each way, and there are 8 daily departures from 8:15am to 5:20pm. The trip will take 1.5-2 hours. There's no specific bus number for this route (like many long-distance buses in China), but you can just go to the bus station and ask to buy tickets to Wuzhen.
Departures from Suzhou South Bus Station (汽车南站 or 苏州南门汽车站), whose entrance is located here at the south west corner of South Ring Road (南环路高架) and Yingchun Road (迎春路). It is unfortunately not on a subway line. The closest subway stop is Tuanjieqiao Station on line 4 from where you can walk to the bus station in 30 minutes. Taxi from the old city area to this bus station will cost just 15-20RMB. The bus to Wuzhen from here costs 36RMB each way and there are 6 daily departures from 8:40am to 4:20pm. The trip will also take 1.5-2 hours.
Which of these buses you take really depend on where you are in the city. If you're north of the old city or on a subway line, then go to the railway station bus station. If you're south of the old city, then go to the south bus station.
Both these buses arrive at Wuzhen Bus Station, from where you can take local bus K350 to get to the scenic areas of Xizha (10 minutes from bus station) and Dongzha (25 minutes from bus station)
Current departure schedule Suzhou -> Wuzhen:
8:15am: departure from Railway Station North Square Bus Station
8:40am: departure from South Bus Station
9:30am: departure from Railway Station North Square Bus Station
10:00am: departure from South Bus Station
10:30am: departure from Railway Station North Square Bus Station
10:55am: departure from South Bus Station
11:30am: departure from Railway Station North Square Bus Station
11:55am: departure from South Bus Station
1:30pm: departure from Railway Station North Square Bus Station
3:00pm: departure from Railway Station North Square Bus Station
3:25pm: departure from South Bus Station
3:55pm: departure from Railway Station North Square Bus Station
4:20pm: departure from South Bus Station
5:20pm: departure from Railway Station North Square Bus Station
Current return schedule Wuzhen -> Suzhou: 8:05am, 9:35am, 10:40am, 12:30pm, 1:30pm, 1:55pm, 2:30pm, 4:00pm, 5:10pm, and 5:30pm
For the most up-to-date schedules, check out the website Chebada.com it's got good bus schedule information in China. It doesn't have English version so you'll need to use Google Translate on it. You can type in "Suzhou" and "Wuzhen" in alphabet to search. Note that I noticed that Google Translate will change "Suzhou South Bus Station" to "Suzhou South Railway Station" because in Chinese it's actually "Suzhou South Station" and we generally refer to railway instead of bus.