You don't need to bring a bike (unless you want to save money on transportation (maybe £40-60 for the duration)). The public transportation in Copenhagen is quite good, and the venue is in walking distance of the central station. Also, there are (electric) bikes available for hourly rental everywhere.
Also check out these hotels - they might not be on hotels.com:
https://www.wakeupcopenhagen.dk/. The Carsten Niebuhrs Gade and Bernstorffsgade ones are within walking distance of the venue