... two hours from Barcelona?... Alquezar is not even in Catalonia anymore!... It's more than two hours for sure, moreover taking into account the last stretch is on county roads. There's a pleasant motorway (A-2) to Lleida, the most western part of Catalonia, then you cross into Aragon and you must take the A-22 motorway to Lascellas, and from there a tiny road A-1229 to Adahuesca, and then the A-1233. I hope you're not visiting in winter, it can be a nightmare if it's snowed.
There's no direct bus from Barcelona to Alquezar --it's far too small to be linked, even to the capital of Aragon: Zaragona. There is one to Barbastro -which is a much bigger town- and from there might be some sort of local service to Alquezar -sorry don't know for sure. Note however it makes a long detour as it goes first to Tarragona, 100km south of Barcelona and then heads north west to Barbastro, in all is a 310km (nearly 200mi) route. Also, there's a bus transfer implied in Tarragona. Check www.alsa.es if you want, and choose "National services".
But I definitively don't recommend going by bus since when you get to Alquezar you'll be "stuck" without a car, and precisely the must-do in the area is to visit the wonderful mountains and valleys of this province, especially the National Park of Sierra y Cañones de Guara, located at the doorstep of the village which has some breath-taking limestone gorges http://www.rednaturaldearagon.com/default.aspx?FolderID=58
Btw, just in case you didn't know, this is the website of Alquezar's townhall: http://www.alquezar.es you might want to email them for specific questions.
Don't expect much people speaking English in that area, it's very rural and most tourism is regional.
PS: Girl, I'm sure there's gotta be a veeery powerful reason to cross the Atlantic just to end up in such remote place, hahaha!