Small regulatory RNAs (srRNAs) are important regulators of gene expression in eukaryotes and prokaryotes. A common motif containing srRNA is a bistable two-gene motif where one gene codes for a transcription factor (TF) which represses the transcription of the second gene, whose transcript is a srRNA which targets the first gene's transcript. Here, we investigate the properties of this motif in a stochastic model which takes the low copy numbers of the RNA components into account. First, we examine the conditions for stability of the two "noisy attractors." We find that for realistic low copy numbers, extreme, but within realistic intervals, mutual repression strengths are required to compensate for the variability of the RNA numbers and thus, achieve long-term bistability. Second, the promoter initiation kinetics is found to strongly influence the bistability of the switch. Super-Poissonian RNA production disrupts the ability of the srRNA to silence its target, though sub-Poissonian RNA production does not rule out the need for strong mutual repression. Finally, we show that asymmetry between the two interactions forming the switch allows an external input to induce the transition from "high srRNA" to "'high TF" more easily (i.e., with a shorter input) than in the opposite direction. We hypothesize that this asymmetric switching property allows these circuits to be more sensitive to one external input, without sacrificing the stability of one of the noisy attractors.