Welcome aboard!
So, first of all: of course your playing sounds bad, you're just starting out!

But don't get discouraged. Beginners are supposed to sound like beginners. You need to be patient and forgiving with yourself. It takes time, practice, and instruction to become a great bass player.
Without seeing or hearing your playing, just taking a total guess here, based on your description of the problem: It sounds like you might not be "muting" the strings properly with your left hand while you are popping with your right hand. Experiment with resting your left-hand fingers against the strings in various locations and with varying degrees of pressure. Can you find a left-hand muting technique that cuts down on the "ringing" sound?
If you don't have a teacher (or even if you do have a teacher, but want a little extra instruction on the side) here is a great how-to slap instructional video. Skip ahead to 4:38 if you want to jump right to the basic popping motion: