I am thinking of going to Bolivia next year. When is the cheapest time to go? Or assuming it is not school holidays, is it all the same?

like youve already guessed , avoiding the standard peak times - like august school holidays and over christmas time is the way to go . Apart from that I suppose booking quite far in advance is the best way of getting best prices - say 4 months plus in advance is a good time range.
Also choosings your route as there are no direct flights from UK to bolivia. A good route to look at is to book direct flights from Madrid to santa cruz or la paz (they will go via santa cruz anyway) and simply use easyjet to get to madrid . Bearing in mind that doing it this way with two seperate connections doesnt give you any protection when one airline decides to change you schedule , so it is worth having a good gap in between to cover yourself - even a few days if you can. I recently got caught with exactly that problem having an air europa flight to madrid rescheduled by two days difference and my easy flights already booked - the rebooking fee with easy jet cost almost the same as the flights.
A good option to look at for Madrid - Bolivia Madrid is with BOA the national bolivian airline - you should be able to get something for around 1000 to 1200usd for a two way flight.

Not so much when+ as to +where. Generally, most of the country is super cheap, altough Santa Cruz is a bit more expensive for food and cab fare, as are staple goods in remote areas / small towns. The only things that vary in price are hotels and bus fare the 1 or 2 days before and after holidays.