Helen, the website for the company that runs the bike tours is:
http://www.realasia.net/
Go for the ABC day tour. Its about 25 quid all in and a great day out!
Any of the big chain hotels are good to stay in Bangkok. Stay somewhere around Sukhumvit Road and your central to most stuff from there.
Make sure you get on the Tuk Tuks for getting about!! Great fun and you can usually get them to race each other off the traffic lights late at night!!!