We will be traveling all over Peru by bus in March. Do you think we will have a problem buying tickets as we go or should we reserve in advance? I would think that since it is not the tourist season we would not have a problem.

I'm not even sure you CAN reserve in advance from overseas...

Many of the bus companies have websites and it appears you can make reservations. I don't speak Spanish but my travel friend does and I thought we could figure it out if Fodorites suggested it. mlgb, from your response are you implying that you traveled in Peru and didn't have a problem making reservations as you went along? Let me know.

No, I just took a local bus. But I took long distance busses in Chile and could not manage any reservations.

Hope someone else can chime in on this..

We were in Peru for 2 months in August and September and really didn't have a problem with booking any of the buses. We used a variety of services long distance, local and tour buses. We speak a little Spoanish which helped but a decent phrasebok would get you by. (Collins Latin American Spanish is excellent).
The exception was the Tour Bus (forget the name) fom Cusco to Puno which we booked a day or two in advance (we could have got tickets from the ordinary bus on the spot.
Go for it! It will very quickly become second nature.

Yes, even the high demand long distance busses that I took in Chile were available within 2 days. My hotel was able to help with reserving, but I still had to go down in person to complete the process.

I can not speak for Peru but I have traveled 1,000's of miles on Buses in Mexico never having a problem getting tickets a hour or so ahead of departure. The only exception was during major holiday time.
PS My Spanish is limited but even before I knew a word I took buses in Mexico with few problems.