If you really only have one day, you might want to consider hiring a private guide. I used this company when I had two days in Bangkok (only used the guide for one day):
http://yourthaiguide.com
They will work with you to fit in everything that is on your "must see" list. You will be able to do a lot more than if you are figuring out all the logistics yourself. I found Bangkok fairly easy to navigate, but some places were very crowded (the palace, for instance) and it was helpful to have someone lead the way and arrange the tickets, etc. The guide picked me up at the hotel, we used public transportation and walking, covering a lot in my one day, and he took me to a delicious place for lunch.