The electric bass uses electromagnetic pickups, to convert string
vibration into electrical energy, and a cord to convey this energy
to an amplifier. The pickup, amplifier input, and cord all interact in a way that greatly influences the final bass sound.
An onboard passive tone control rolls off highs by applying a capacitor from the instruments "hot" signal to ground.
Surprice, your cable has capacitance, too, which has the same electrical effect as adding another tone knob. While this capacitance is not nearly as much as a tone control's, it's significant in some situations. Whether this has a major effect depends on two other factors, amp-input impedance and bass-output impedance.
When sending a signal to an amplifier (or mixer), some of the signal gets lost due to the amp's input impedance, which is specified in ohms (a resistance unit) or kohms ("k" for short, which stands for thousands of ohms). With passive bass pickups, lower amp-input impedances load down the bass and produce a duller sound. (Tubes have inherently high-input impedances, which might partially account for their enduring popularity).
Impedance doesn't affect just level, the higher the impedance, the greater the tone control's effect. This is why a tone knob on a bass can seem very effective with some amps and not with others. Cable capacitance is also more of an issue with higher input impedances.
An input impedance of 250k or higher will have virtually no effect on your signal. Between 100k and 250k there can be slight, almost imperceptible dulling of the sound. Under 50k the sound will be obviously compromised, 10k-and-less impedances, common in pro-level signal processors and amps, will load down your signal big-time.
As you can see in the diagram below, the impedance surely isn't consistent over the entire audio spectrum. It greatly "swings" from one value to another as the frequency changes.
The diagram below is a typical speaker (driver) impedance curve.
An instrument's output impedance is equivalent to adding a resistor in series with the bass, lowering volume somewhat. Almost all stock pickups have a relatively high output impedance (around 10kohms), while active pickups have a low output impedance (under 1kohm).
Note that high output impedances make cable-capacitance effects more noticable.
Furthermore, the bass-output impedance and amp-input impedance interact. Generally you want a very high amp-input impedance if you're using stock pickups, as this minimizes signal loss (especially in the high frequencies ).
Active pickups, which have lower output impedances, are realtively immune to an amp's input impedance.
The Bottom Line
If you want a bass setup that sounds pretty much the same regarless of the cable you're using, consider replacing your passive pickups with actives. Or, feed your bass into an effect (preamp, compressor, buffer, etc.) with a high input impedance.
If you're committed to using a stock bass and high-impedance amp, keep your cord as short as possible, as a longer cable means more cable capacitance.
Cable specs include a figure for capacitance, usually specified in picofarads (pF) per foor, choose a cable with the lowest pF-per-foot rating. (Paradoxially, heavy-duty cables often have a higher capacitance than lightweight ones). Avoid coil cords, and keep your onboard volume control as high as possible.