I'm traveling to Perú and I want to buy a bus ticket from Arequipa to Nazca.
Does there exists a web site where I can get my tickets before arriving to Arequipa?
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As a peruvian, I can assure that you can buy the tickets before arriving to the city through the websites listed by @JoErNano or any other you may found on internet.
And additionally, I would suggest you to buy the tickets from well known companies, as OLTURSA (I traveled with this one and it's really comfortable and not so expensive), Cruz del Sur (This is good but a bit expensive), Ormeño, etc
Why? Because not every company is reliable when it comes to puntuality, comfortability, security, etc.
This doesn't mean that you won't suffer of any of this things but is less probable.
You can get cross prices with various of good companies on this link
Ps: Be sure that there is a direct route from where you are to where you want to go, sometimes that there is no direct route and you may need to use some local transports like public taxis , taxi motos, or make connections through differents buses.
Ps2: About @blackbird57 query , I believe that if you buy it on the local currency (soles) there won't be any extra charge, but if you buy it with your own currency (it will be changed as their will) which is probably, because paying through the website is with credit cards, the price may raise a bit. It's always "cheaper" to buy with soles, unless you buy on not so reliable companies which may give you a "gringo" rate.
Rome2Rio says there are three bus companies running the Arequipa - Nazca route. You are looking at a total journey time of approximately 9 hours. Below are the company websites which can be used to purchase the tickets:
I was in Peru several months ago. I went from Arequipa to Ica. I just walked into the bus station in the morning and bought a ticket for that night. I bought a first class ticket and slept overnight on a big comfy chair. A simple dinner and breakfast was also served.
Buying a ticket there and then worked well for me, but I'm not sure if there's festivals happening when you're travelling.
I highly recommend the sand dunes of Huacachina