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.
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