Most budget trip's option is a bus. It is cheaper than train, and by time is going about the same. The main disadvantage is a necessity to spend 10-14 hours in sitting position. From advantages - bigger amount of stops in different Latvia's cities. Also buses got more destinations in comparison with a train. You can go to different cities in Europe by bus.

There are bus connections from Riga to virtually any point in Europe, Russia, Ukraine and Belarus.

Useful links:

Riga bus station (LV, RU, EN, GER)

Bus itineraries: quick search (LV, EN, RU)

Ecolines coach service (EN, RU, LV, LT, PL, DE, BG, EE)

Eurolines coach service (LV, EN, RU)

Nordeka coach service (LV, EN, RU)