If the two coils are not wired together in series already, plus you have four dangling wires instead of three, I'd check that they will hum cancel when used together first. (They may not be from the same pickup originally). The easiest way is to see if the tops of the bobbins attract magnetically. If they don't you can either use one bobbin upside down, or if they have ceramic magnets, you can remove one, flip it and reglue it.
You should definitely test the DC resistance with your multimeter. Each coil should be in the region of 2-6 kOhms, and the coils should be within 10% of one another.
If the coils are magnetically opposite, then next you need to wire them so that their signals are in phase. The way to determine phase is to connect your multimeter across each coil and measure the polarity of the voltage that is produced as you remove a little screwdriver or nail or something that is attached to the magnets. You'll need to set the meter to millivolts DC. Negative on pull-off is
sort of the standard. (FWIW, it doesn't really matter whether you get a positive reading or a negative on "pull-off", just as long as both coils are the same.) Mark each coil lead that had the black probe connected with a piece of tape or something. For the moment, call these "negative" leads.
Now you have to work out which wire is the start and which is the finish of each coil.
It helps shield the pickup if the output lead connected to the outermost winding is grounded.
I'm afraid this is a common myth. With exposed pole pieces in a simple/vintage fender design, it's important to actually have the
inner windings at earth, otherwise you'll have a buzz whenever you brush the tops of your pickups with your fingers. And copper taping the outside of the coil, or running the outer windings at earth potential, makes little or no difference to the shielding of the coil. (Some say that they can hear a difference in tone when a coil is reversed due to capacitance, but I can't and that's really getting OT)
You can just remove the cover and look, but that can be hard, especially if the pickup is potted. So the best way is to connect each coil to an amp (solder it to a jack or aligator clip it to a guitar lead). The wire that you marked with tape should be connected to the sleeve of the jack. Avoid touching any exposed metal solder lugs or wire and turn up the amp till you start to hear a little single coil hum. Then carefully touch the tops of the magnets and if you get a louder buzz, then you'll need to wire these in reverse to this when you put them in the bass, so you can go ahead and call the wire from each coil that you marked with tape as "positive" instead of "negative".
Finally, you need to decide which coil you are most likely to touch while playing. THis is because only one will be silent when you touch the magnets when the two are in series. For me it's the E/A coil because I rest my thumb on the E string just there. (If your hand is nowhere near the pickup when you play, or you plan to use non-hole type covers, or perhaps you plan to earth the magnets in some way, I guess you could skip all this, but it doesn't hurt to get it right.) Some pick players tend to touch the D/G coil with their ring and little fingers.
Now that you know which wire goes to the start of the wind, the phase of the coils, and that they actually will humcancel with eachother, you should mark the bobbin with + and - or something and remove the original single wires. You should use shielded wire for pickups, and that matter, any hi-Z signal wire that's more than an inch long.
