In improvisation, there are three elements of speed: the speed of aural comprehension, physical execution, and imaginativecreativity.
Attention to each is critical to successful jazz. Most musicians spend the majority of their practice time on the speed of execution. However, musical artistry is more than muscle memory.
It is critical that you spend an equal amount of time developing the other two aspects (which are often ignored or unknown). The speed of comprehension is achieved by training your ear to quickly understand what you hear, whether the sound is imagined or from other musicians. Then, you must be able to play what you hear on your instrument.
Also, you must work on how fast you can access your imagination on the spot. It is much easier to create a solo on a blues with a metronome marking of 120 than 220. The slower tempo gives you more room. When it is fast, you have less time to integrate all three aspects. If the speed of recognizing what you hear is slow, you won’t be able to find it on your instrument in real time.
Often, when musicians don’t hear ideas in their head and play anyways, they will move their fingers without having a clear or articulated idea. The results will sound vagrant; sounds without a home. You must be able to have an idea in your head and know where to find it on your instrument immediately. The goal is to woodshed on all three speeds separately until they are roughly the same. I highly recommend isolating each speed until it is fast and fluid in execution.
In improvisation, you have to be able to comprehend, create, and execute in milliseconds. One exercise I recommend to all serious improvisers is to play a given tune at 90 BPM, 130 BPM, 160 BPM, and 200 BPM. I have found that starting with a very slow BPM gives you more space for your imagination; then increase tempo from there. Focusing on all three elements will help you not only to play what you hear and do it at faster tempos, but make you a better improviser all around. Record yourself playing a couple of choruses at each speed, then listen and assess for effectiveness.