An additional trouble... when I strike a note without any of the other instruments being played, there is a slight hiss as soon as the note is heard and the hiss stops when the note can no longer be heard.
Still could be the earbud's fit and seal or just the design of the earbud drivers. But if the kick sounds good w/ healthy low end, there's probably something else going on.
The hiss you describe sounds like the signal chain involves a noise gate, and possibly compression. Your OP sounds like you're sending the bass via DI to the mixer, and the PSM 300 is being fed from an aux send (or in stereo from a pair of auxes). If that's so, have you talked w/ whoever is operating the board about how the bass channel is being processed?
Before I went out and bought anything I'd want to hear the bass fed w/o additional processing or eq back into the Shure transmitter. That is, disable whatever is happening at the board on your channel other than gain.
Then listen to the bass via the board's headphone out using your buds. If that doesn't sound good, try listening w/ headphones from the board. If it's bad w/ buds but fine with headphones, then your buds are the problem. If it's bad with buds and w/ headphones, then the problem is either with the mixer channel or upstream b/w bass and board.
OTOH, if when you disable any inserts and processing on your bass's mixer channel, your earbuds sound good from the mixing board's headphone output, then try monitoring via the Shure. If you get good sound via the board but lose the bass via the transmitter/receiver, then the problem might be the gain structure, your IEM limiter settings, or a problem w/ the transmitter or reciever. (TBH, neither IEM hardware malfunction nor an overly active IEM limiter seems likely, b/c the kick drum and the rest of the mix aren't compromised, but stranger things happen.)