Is there a way to check the timetable of the bullet trains from Suzhou to Beijing?

Yes, of course, you can check the timetable with the train schedule search tool on the train pare of this website, where you will find all the detailed info, and you can book the tickets through it.

Here is some info about the train timetable, which may be useful for you. From 07:34 to 17:55, there are almost 20 trains available. The duration is about 5 hours, and the fare is CNY 523.5 for a second class seat and CNY 883.5 for the first class seat.

All the bullet trains depart from North Railway Station, which is located on Fulin Road, Xiangcheng District, and you can live in a hotel near that train station. But it seems the cloest one is even around 10min away.