In order to probe the physical conditions in the high-pressure environments of galactic bulges, we have studied the properties of the dense molecular gas in the bulges of a sample of 19 mostly normal spiral galaxies. We observed the 3 mm emission from the molecules HCN and CS, which trace gas densities of approximately 10(5) cm-3. Our high detection rate (68% in HCN, 50% in CS) suggests that most spiral galaxies, not just starburst galaxies, contain appreciable quantities of dense gas in their bulges. The HCN to CO ratio of integrated intensities R(HCN,CO) measured in the bulges of galaxies can be very sensitive to the resolution of the radio beam used for the observations; the ratio tends to be significantly higher for telescopes with smaller beams. The CS to CO ratios R(CS,CO) measured in extragalactic bulges are consistent with that measured over the Milky Way bulge but appear to be at least a factor of 2 larger than in local GMCs in the Galactic disk. Since R(CS,CO) in local GMCs is likely to be an upper limit of the average R(CS,CO) in the disk of the Milky Way, we conclude that nuclear molecular clouds are not like disk molecular clouds. Despite the similar critical excitation densities of the two molecules used to trace dense gas in this study, we find that the HCN emission is consistently brighter than the CS in these sources by an average of 2.4 in the integrated intensities.