The tuner's task is inherently problematic. What makes a tuner good is not the degree of accuracy, because even the cheapest tuners (if they are calibrated) will be far more accurate in measuring a clean tone that any ear can tell. People crowing about the gee-whiz .001-cent accuracy of their tuners are being ignorant because not only can you not hear that level of accuracy, but your guitar can't produce a stable enough tone to take advantage of such accuracy even if it mattered.
What makes a good tuner is how well its algorithm damps and translates an unstable tone, and -- as you point out -- the note from the guitar is not stable, particular on the larger strings (bass is absolute hell in this regard). Even this is a compromise, usually a bad one.
There's a great article by multi-platinum engineer Jack Endino about the impossibility of a played guitar ever really being in tune at all. I've linked to it here before. The problem isn't with the tuner, it's with the instrument.
Then there's the whole heated issue of temperament.
The best guitar tuner at any price is probably
G-Tune 2.51. If there's a better one, I've never seen or heard of it. The best thing about G-Tune is that it graphically demonstrates the problems described with the unstable tone from the guitar. You need a clean sine wave to get a meaningful reading, and the guitar doesn't produce it on a lot of notes. By watching the oscilloscope function, you can at least find the least-unstable options among the various-fret harmonics and try to get a meaningful tuning from that.
Tuning a guitar (much less a bass) will always be a compromise and never entirely successful.
Don't blame the tuner.
