What kind of amp are you using and how high was the volume? Some hum can be “normal” at high volume, but as @JT said, it may be an electrical issue. Check to see if your amp has a ground lift, and try toggling it to see if it makes any difference.
Sounds more like a feedback issue to me if the hum goes away when you change direction.
Good luck . . . 
Cheers
Joe
I’d concur Joe,
Jacob what you have is called a ‘precision’ style pick up and technically it is referred to as a ‘split-coil’. The design of the split coils helps to reduce noise in a similar way to a humbucker. The other type found on Jazz Bass style guitars is a ‘single coil’ (looks like a long straight bar, not staggered like yours) and these are more prone to interference. Unless you have physically developed a fault in your bass (unlikely) it’s probably not that so I’d turn your attention to the amp/other electronics as others have said. Good luck.
Playing in isolation is the hardest critic (aside from listening/watching yourself on video!).
Remember, in a band setting lots of what you hear won’t be heard.
Listen to some really good bassists play in isolation. Hear how they sound, you won’t strive for absolute perfection any longer. Not that technique is not important, more so on recording vs. live, but don’t beat yourself up.
Hum, happens, lots of factors, really bad hum might mean a bad connection, or ground or other, esp in an older bass. A tech can sort it out.
That would be my guess as well. You may just be getting a hum from your pickup when it’s pointed towards your amp or other electronics.
The hum will be directional depending on two things.
Where the gaps in your shielding are (typically the pickups)
Where the interference is coming from. (something electric or electronic)
Pretty much any of my basses in single coil mode will hum in my living room if I face the amp. However, it’s right beside a heap of other entertainment gear, so this isn’t surprising.
HOWEVER, they stop humming at different points of the compass as I turn away from that most humming direction. Some basses are quiet at about 45 degrees of the noisiest position. Others are good at 90. Once I face past 90 degrees on almost all my basses, everything is pretty quiet, but it’s quite a distance to anything significantly electrical at that point.
Power metres with the spinning disks are by far the worst things in most houses for electromagnetic interference. I also had a touch lamp that introduced incredible noise into the entire circuit that it was on. Even turned off, the squeal it made through a UHF radio was quite impressive.
(Then there was the time I discovered that I could reboot my computer with the 5 watt UHF walkie talkie, if the computer had the side off and I was close to it doing radio checks… )
In my computer room, I’m surrounded on three sides by computers and directly across from the amp is the power meter outside.
I really notice directional hum in here. It seems to mostly come from the power meter as it’s over my right shoulder and goes quiet while I’m practicing while watching the screen.
By far the most resistant pickups I have are the Fishman Fluences. I can only make them pick up interference if they’re singly selected and single coil in either room.
I didn’t shield anything, just to see if the advertising blurb was real.
It is.
It could be because of the same reason rotating an antenna tunes in a radio station better or worse. The bass can act like an antenna. Noise sources can transmit that noise just like a radio station. When things are aligned, it gets picked up.
I couldn’t figure it out. It’s a laney amp. It’s more noticeable the higher the volume. It might be caused by some electronics the neighbours use, cause I tried unplugging absolutely everything and tried moving my amp to the other side of me and it made no difference. The hum is most noticeable when I point it towards one side of the room, no matter where the amp is.
Is it where your computer is? Or a TV?
None, I’ve unplugged everything and tried moving stuff too.
I personally think your 30 year old Ibanez bass could be the cause since the hum isn’t always there when you mentioned it in your original post. Just FYI some amps have a noticeable hum when you turn them up.
Maybe use a better quality cable or maybe have someone with a modern electric guitar/bass plug it in and see if there is any difference?
I look at the world
And I notice it’s turning
While my (bass) guitar gently hums.
A-HA!
Is your power meter on the wall outside?
When I worked at the computer fair, a guy came back to complain about his monitor shimmering. This was back in the CRT days. I told him to move his computer either 2 metres to the right, or two metres to the left. I refused to explain to him why, but insisted that he do it before bringing it back.
He came back the next month and demanded to know why moving it solved the problem.
I asked him to go and look where he power meter was…
I have a new practice amp for my mini stack in the computer room. It’s significantly quieter with the previously noisiest bass now. Maybe the Roland Bass Cube 100 didn’t like where it was? It was replaced with a Peavey Mini Mega. This thing is LOUD. And very quiet…
I’m not saying it’s aliens, but it’s probably aliens. 
When you point the bass away from the music it can’t see the words, so it hums.
I’ll get my coat…