Is there a bus that travel from Bogota to Quito to Lima to Santiago?
On each of the 4 countries you plan to travel, bus companies will offer international service because they have connections with neighboring countries. For example you can take a bus from Lima to Buenos Aires and you will change to a different bus when traveling on a different country, but you buy only one ticket. I would recomend that you make shorter distances each time because it’s a loooonnnngggg way from Bogota to Santiago. I did a non-stop bus trip from Lima to Santiago when I was 17 and I would never do it again, unles maybe on a Bed-Bus (they didn’t exist at the time). From Bogota to Quito is the shortest distance (around 500 miles or 10 hours by bus) between the two capitals is the city of Cali famous for beautiful women. I don’t think it’s necesary to book-in in advance and always take the best bus company specially in Colombia, Ecuador and Peru (ask in each country for the best) in Peru I would recomend LINEA, CRUZ DEL SUR and OLTURSA. From Quito to Lima it must be like 1,00