The holy grail of upright bass omni microphones is the old vintage altec lipstick or cokebottle tube mic often wrapped in a bit of foam and stuck with capsule just under the edge of the fingerboard. I've had great success with mine. Bruce Swedien name drops these mics everytime someone asks him about his upright bass sounds, he certainly knows what he's talking about.
I also have used just about every other classic microphone ever made in this application and other standout favorites are Gefell CMV563 with omni, figure 8, or cardioid (M7) capsules (they all give really different flavors), Neumann U67, AKG C12, Neumann U47, Chameleon Labs TS1 and TS2 models, Sennheiser 441, Shinybox ribbon (figure 8 as all ribbons are), etc. I do not like the AKG D12 or D112 (both very different from each other) in this application, nor do I like the Sennheiser 421, all 3 mics often used by others. All studio mics at various price points.
Figure 8 is often a great choice for upright also as it will diminish some of the room sound and there is some real magic in the deep lows of many figure 8 ribbons that just matches well with bass. Also it has the most pronounced proximity effect which can help (or hinder) depending on placement and playing.
If you like the SM58 (I hated it when I've tried it on my upright) then what you might be liking is the focused mids. With such a personal instrument as the upright it is very much like recording vocals in the studio, results will vary from person to person so hearing about other's particular setups will only get you in the ballpark but may not be perfect for you. For example, it is well known that Bono from U2 uses an SM58 as his vocal mic in the studio, a practice that would make most other artists and engineers cringe, but it is the perfect match for the tonal qualities of his voice.
Generally the more distance you can get from the upright the better it will sound if you have a really good (or really really really dead) room. As you move the mic away you start getting a lot less of the direct sound and more of the room sound, in the studio we often talk about "playing the room" and how the room is just as important (or more) to the sound as the instrument and the recording equipment.
A very good starting point for mic placement is to put a mic where your ears are and see how close it gets to what you are actually hearing yourself. Then you have a basis to make adjustments. Many times movements of inches make huge differences.
Here's figure 8 pattern with gut strings and some decent distance, about 4 or 5 feet, in a not-so-good room...
Here's omni pattern with guts, placement a couple feet out, slightly higher than the finger contact toward the fingerboard, you can still hear a lot of the room...
Here's cardioid, steel strings, up relatively close (about a foot or foot and a half up and back from the treble F hole but pointed to the left of the hole, not at it)...
Here's some bowing with omni, pretty close in, same setup as the cardioid example above, you can still hear a bit of the room, but not nearly as much as the other omni example that has more distance...
Pic of CMV563 with the omni capsule in one of the sweet spots for me and my bass that seems to work well...
