  We describe GBTrans, a real-time search system designed to find fast radio
bursts (FRBs) using the 20-m radio telescope at the Green Bank Observatory. The
telescope has been part of the Skynet educational program since 2015. We give
details of the observing system and report on the non-detection of FRBs from a
total observing time of 503 days. Single pulses from four known pulsars were
detected as part of the commensal observing. The system is sensitive enough to
detect approximately half of all currently known FRBs and we estimate that our
survey probed redshifts out to about 0.3 corresponding to an effective survey
volume of around 124,000~Mpc$^3$. Modeling the FRB rate as a function of
fluence, $F$, as a power law with $F^{-\alpha}$, we constrain the index $\alpha
< 2.5$ at the 90% confidence level. We discuss the implications of this result
in the context of constraints from other FRB surveys.
