Below is a list of hostels, guest houses, and B&Bs either in S. Queensferry or that are an easy car-free journey away (I've noted which places have parking, however Edinburgh is not a very car-freindly city)  I've tried to generally limit the search to places quite convienent for getting to the site as well as seeing Edinburgh... 

In S. Queensferry
aka within walking distance of the event site...

Number 18 Guest House seems to be the cheapest on offer (and is the only one in the "under £35 per night" price range I looked for, the other places I saw in Queensferry were £50 to £60 per night); it would be a few blocks from the event site and should be either right on or quite close to the bus into Edinburgh.  http://www.number18.org.uk/

In Edinburgh itself
(more convienent for most sightseeing)

The Caledonian youth hostel is right on the First 43 bus route (First busses are white with pink and purple trim, there's 3-4 bus companies acting in Edinburgh, but they luckilly all use the same stops!),  which would make it reasonably convienent to get you to the event... and since it's down town, you'd have an easier time getting to Sunday's museaum trip, and to anything in Edinburgh you'd like to see. 
http://www.caledonianbackpackers.net/

City Centre Guest House hostel looks to be a short walk from the correct bus stop, and is also right downtown... it also has the option of double/twin rooms, so would be a good compromise between privacy, cheapness, and convience for both normal tourist stuff and Dance Moot.
http://www.citycentreguesthouse.co.uk/

This one is opposite Haymarket train station, and would have good bus routes to tourist Edinburgh.  It would be a 15-20 min walk to the bus for S Queensferry (the 43) if you don't want to take the train there and walk down the hill...
http://www.edinburghcitycentrehostels.co.uk/

This hostel is quite convienent for downtown Edinburgh, and a 3-4 block walk to where the bus to Dance Moot is... they also have private rooms.
http://www.smartcityhostels.com/home.html

There are another half-dozen youth hostels in Edinburgh, if none of these suite...

There are also about a million-billion (as my 3 year old nephew might say!) B&Bs in Edinbugh.  That said, I'm not seeing B&Bs that are right in downtown Edinburgh and still on the "correct bus route", but here are a few other options...

My (Estevana's) parents stay with Duncan and Elaine all the time, they are loveley people and it's a really nice B&B, a 15min bus ride for most tourist stuff and for the event, you'd need to take one bus to get downtown, then transfer to the 43 or the train.  I don't *think* they have parking because we always just take the bus.
http://www.glendaleguesthouse.co.uk/

These two B&Bs are on the correct bus route, but a bit out of town, so you'd probalby want to take a bus to see Edinburgh itself (or walk 30-40min...).  Though they do have parking at the B&B, parking in Edinburgh proper is a bit of a nightmare.
http://www.acerlodge.co.uk/index.htm
http://sandilandshouse.co.uk/

On the same road, but even further out (I'd recommend cycling or taking the bus into town, though they do have parking available):
http://www.iknow-scotland.co.uk/accommodation/18434-stewarts_b_and_b-edinburgh.htm
http://www.bluebutterflybb.co.uk/