Wailking is the best option to visit the main attractions of the city, but there are some places of interest you can take public transportation or rent a bike to get there.
By taxi
Official taxis are white, and have a reddish stripe on the front door. The tariff is displayed on top of the car a 1 during daytime, a 2 during the night, which become 2 and 3 on holidays such as Christmas Eve. You can take taxis in the taxi ranks all around the city (http://www.aytoburgos.es/...), also you can call in advance +34 947 277777 or +34 947 481010.
By car
Transportation by private car in Burgos is not difficult. Altough looking for a place to park in the city center can be very time consuming unless you park in private parkings.
By bike
Bicycle is a good option for visiting all atractions of the city. Burgos has a very good bicycle lane that connects several points of the town. Also there is a public rent service for bikes called bicibur (http://www.bicibur.es/). Riding a bicycle in Burgos is a good activity, there are no big slopes and riding along the rivers or in Fuentes Blancas are very interesting activities.
By bus
Burgos has an extensive system of city buses (http://www.aytoburgos.es/...), which you can ride for just 85 cents. You can buy the ticket on board.