Another option that is totally worth checking out is the boats that run in the canals. Fares depend on the length on your journey (I paid 9.50 Baht from the Ratchathewi district with all the shopping malls to stop Phanfa Bridge which is a 10 min walk from Khaosan Road). You might have to walk from and to the boat stop a bit. However, considering the crazy traffic jams in Bangkok you might be even with that bit of walking quicker.
(Photo by Frida Aguilar Estrada on Unsplash)