Among several mechanisms involved in the plant stress response, synthesis of guanosine tetra and pentaphosphates (alarmones), homologous to the bacterial stringent response, is of crucial importance. Plant alarmones affect, among others, photosynthetic activity, metabolite accumulation, and nutrient remobilization, and thus regulate plant growth and development. The plant RSH (RelA/SpoT homolog) genes, that encode synthetases and/or hydrolases of alarmones, have been characterized in a limited number of plant species, e.g., Arabidopsis thaliana, Oryza sativa, and Ipomoea nil. Here, we used dry-to-wet laboratory research approaches to characterize RSH family genes in the polyploid plant Brassica napus. There are 12 RSH genes in the genome of rapeseed that belong to four types of RSH genes: 6 RSH1, 2 RSH2, 3 RSH3, and 1 CRSH. BnRSH genes contain 13–24 introns in RSH1, 2–6 introns in RSH2, 1–6 introns in RSH3, and 2–3 introns in the CRSH genes. In the promoter regions of the RSH genes, we showed the presence of regulatory elements of the response to light, plant hormones, plant development, and abiotic and biotic stresses. The wet-lab analysis showed that expression of BnRSH genes is generally not significantly affected by salt stress, but that the presence of PGPR bacteria, mostly of Serratia sp., increased the expression of BnRSH significantly. The obtained results show that BnRSH genes are differently affected by biotic and abiotic factors, which indicates their different functions in plants.