Many people are skeptical of using guitar pickups on bass. And it is true that many of the aftermarket guitar pickups do not produce a pleasing tone when used with a bass guitar. But the reason for this is that many of the aftermarket guitar pickups are intentionally overwound, which produces a strong midrange emphasis, at the expense of low and high frequencies. And "midrange" to a guitarist winds up being "high midrange" for a bassist, which explains the unpleasant tonal profile and thus the poor reputation they have amongst our community.
However, the physics behind guitar pickups is exactly the same physics that makes bass pickups work. They are all essentially coils of wire wound around magnetic poles (or magnetized slugs). Nothing sophisticated at work here. Couple this with the fact that electric bass guitars are very, very similar to electric guitars - the only real difference is that one produces notes about an octave below the other. They both use ferrous strings that excite the magnetic field(s) of the pickup(s). Therefore, a guitar pickup will produce a signal when a bass string excites it, and a bass pickup will do the same if used on a guitar.
Where the differences lie is primarily in the typical tonal goals. Most rock/metal guitarists like that overdriven, saturated, mid-heavy sound, as it interacts well with their effects and amplifiers. However, many guitarists have very different goals; many working in the country/folk/jazz realms value a flat frequency response, in which the full spectrum of the plucked string is reproduced and transmitted as faithfully as possible. And guess what - pickups designed to produce a flat response on guitar are also very, very likely to produce a flat response when used on a bass guitar!
Bill & Becky Lawrence's pickups (marketed under the "Wilde" brand name) fall into this latter category. One of Bill's fundamental design goals throughout his many years as a pickup maker was a clear, full-spectrum tone; his pickups are designed to recreate the natural sound of the string. And that they do, as anyone using his P46/J45 pickups can tell you. But his guitar pickups are also built to that same end.
I recently built myself a Flying V bass. I wrote to Becky at Wilde and asked her about using some of Bill's designs in the V. Her reply was that Bill always felt like the L90, in its 4H incarnation, would make a great bass pickup. So I ordered a pair, installed them, and wow, what a tone! Full, clear, and loud! Now I'm considering building a G3-inspired bass using a triplet of L45s...
In truth, the modern distinction between "guitar" pickups and "bass" pickups has more to do with the available form factors for retrofitting, than actual tone (the obvious exception being the afore-mentioned overwound, "mid-focused" pickups). Any "guitar" pickup with a reasonably flat tonal profile should perform well on bass guitar. Don't discount unusual options simply because they're unusual!
