Those bartolini pickups are essentially symmetrical, it won't make a difference. You can flip flop all day long.
In fact, it generally doesn't make a difference, or when it does, the difference isn't inherently good or bad, it's just (ever so slightly) different.
Some pickups are a single coil, under all the strings. The coil itself is "symmetrical" by default, and typically, for basses, the magnet structure (blade, pole, bar under steel slugs, whatever) is symmetrical. We don't do silly things with bass pickups like people sometimes do with guitar pickups, i.e. a strat pickup with pole heights staggered non-symmetrically. So - single coil pickups "don't care" which way around they are.
That leaves humbuckers.
Stacked coil humbuckers are the easiest to describe - two coils right on top of each other. Basically a single coil pickup, but the coil wire switches direction halfway through to cause humbucking operation. They behave like singles in this respect - no difference.
On most soapbar sized humbuckers, there are two coils, next to each other, such that all strings are over both (think: two J pickups in the same cover). In many of these pickups, the two coils are 100% identical. Once again, it literally won't matter which way you put the pickup. On a very small number of this style of pickup, the two coils will not be identical - sometimes the magnet is different in each coil, or sometimes one coil won't even have a magnet (it'll have a steel blade, or sometimes nothing at all, and it's only role will be hum cancelling). In these non-symmetrical pickups, there can be a very small theoretical difference in tone by flip flopping the pickup. The two coils will have slightly different tonal impacts and outputs, and flip flopping the pickup will put them in slightly different positions under the strings. The difference would be, at most, on the order of magnitude of the difference between a 60's J bridge position and a 70's J bridge position, though in practice I've found the difference to often be so small that no one in their right mind would claim to even hear it.
Other humbuckers are two coils end to end, like a P pickup, but with or without offset. In nearly all cases, the coils are identical, and it won't matter at all. Most "noiseless" J's that aren't stacked coils are inline humbuckers like this. In some edge cases (like, a 5 string pickup) the coils are pretty different, and it can make a difference in the string to string balance in terms of output and tone.
Sidewinder pickups are effectively a stacked coil pickup laid on it's side, with a magnet structure to point the field up towards the string. They're just as symmetrical as a stacked coil and behave the same.
Still other humbuckers are even stranger arrangements (single coil per string, two pairs of inline coils next to each other, to make a "quad", and so on) but I have yet to see any of those pickups where things were not symmetrical, so it wouldn't make a difference.
So, yeah, it doesn't make a difference.
I'm speaking as a lefty who struggled to understand this early on for myself, since it's super frustrating to install "right handed" pickups the "correct" way in a lefty instrument and have the wiring leave the pickup on the "wrong" side of the pickup. When I work on lefty instruments these days, I just orient the pickups in a way that makes sense. Sometimes this results in funny situations, like a prominent logo ("bartolini" across the top of their pickups, for instance) is upside down. As far as I'm concerned, that just adds character. These days, I make all of my own pickups, so I just make the ones for my own lefty basses (and some lefty customer's basses) as "left handed" pickups, such that the wiring and screw holes are appropriate for a left handed bass. Or in some cases I've deliberately done things that look funny as a way to "silently protest" the right-hand-dominated world we live in, like this:
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At the end of the day, it's really just a fun quirk and definitely not a serious concern in the least. Orient the pickups in the way that makes sense and enjoy!
