There are two types of ED Visas. The first type of ED visa is for studying Thai language, kickboxing, scuba diving, or other informal activities. A person can only study for one year on this visa.
The other type is for a formal degree seeking student. This visa allows a person to stay in Thailand for the course of the program (2 years in your case, I think). The extension of stays will be issued each term.
Your hotel should know exactly what type of document Bangkok Immigration requires. If they don't, I recommend contacting the Tourist Authority of Thailand, they should know or be able to speak to the hotel for the document
Did you enter via Phuket? I remember someone recently who entered on an STV via Phuket, and had a problem getting the 90 day extension of stay based on STV in Bangkok because the hotel didn't know about the certificate