I don't know about buses, but even if they exist they can't offer better timetable than trains. Trains are leaving almost every hour from Leipsic to Dresden and to Prague.
Taking advantage of the Sachsen-Böhmen Ticket the 2 of you can travel from Leipzig to Prague for 28,5 EUR. That's 14.25 EUR/person. I doubt the bus can beat this, not to mention trains are much more comfortable and take a beautiful route along the Elbe river and not the motorway.
The catch is, you can use only regional trains in Germany(RE, RB, S-Bahn), but any train in the Czech Republic.
Sorry, actually that ticket covers you only as far as Usti nad Labem. You must add 250 CZK for the 2 of you from Usti nad Labem till Prague. Thats about 10 EUR or 5 EUR each. The total is still below 20 EUR/person!
You must change trains 3 times: in Dresden , Bad Schandau and Decin. Keep in mind that you have to buy tickets in Decin only for the section between Usti nad Labem - Praha as between Decin and Usti nad Labem the Sachsen-Böhmen Ticket is valid. If the conductor comes show her both tickets.
On the way back I recommend you a romantic steamboat trip down the Elbe from Bad Schandau to Pirna or Pillnitz and continue by train to Leipzig.
http://www.saechsische-dampfschiffahrt.de/index-en.html
http://www.raildude.com/en/train-ticket-country/sachsen-b%C3%B6hmen-ticket/germany/56
http://en.wikipedia.org/wiki/Dresden%E2%80%93D%C4%9B%C4%8D%C3%ADn_railway
http://en.wikipedia.org/wiki/Saxon_Switzerland
http://en.wikipedia.org/wiki/Pillnitz