Is 2000 per month enough for 1 bdrm in SIP Suzhou

There are options within your housing allowance, in SIP. It's all about where exactly you preferentially intend to stay in SIP and for how long?
With these 2 questions you should be able to find whether you are within the allowance or not.
I check the apartments on the spot, cause here there is a high demand for cheap apartments by the locals. So normally the cheap apartments get full in no time.
However, owners of high-end aparmtents are normally well-educated and rich, so they look for a talented agent to sell their property on a great website. So on websites you'll see high-end apartments (> 4,000 yuan).
Unfortunately, I lost all my contacts, if I were you, I'll sleep for some nights in a hotel nearby my workplace and hopefully during this time I'll befriend the locals in my workplace and around to help me out with finding apartments below 2,000 yuan. That's the best way to also integrate the culture. You'll have to adapt to this sort of thing rather than the typical way we logically do of: planning our visits.

No, and it's very common for them to lowball housing allowance for low end expat jobs.