There is a difference between percussive and continuous-tone instruments: percussive instruments (like a piano or a plucked bass or even a bass drum or its more defined cousin kettle drum) start with a rather prominent part of the vibration while continuous-tone instruments have to build up the the energy of their sustained operation first. So bass recorders and wind pipes (organ) are among those with the slowest attack. Reed instruments like bassoons are faster starters.
However, many instruments with a comparatively poignant primary oscillator then feed some resonator, and a resonator still needs to pump up its energy over several oscillations before being in full swing, and in order to resonate, its operation already includes a mechanical delay for one cycle time that retains a significant amount of energy.
So there is a basic slowness for the development of the actual sound. There also is a basic time/frequency unsharpness relation that limits how fast pitch differences can be determined: this is a mathematical rather than a physical limit. And finally the detection in the inner ear again works with a semi-resonant contraption relying on a delay line introducing some frequency-related delay to reliable detection.
This is ameliorated somewhat by the listener not making sense of his hearing in real-time but with some delay of perception that allows reconciling faster and slower detected features.
This particularly helps with percussive instruments where a poignant attack gives a good location in time and the associated pitch can be determined only later. Trills, coloratura, tonally specific fast runs and phrases are still usually not working well for the listener in the lower ranges of bass instruments.