If you would play plugged in anyway, perhaps getting an acoustic bass is optional. If it's acceptable to play an electric bass, this frees up your budget for a proper amp.
You have four options:
1. Battery-powered combo.
2. Small head powered with a DC brick.
3. Ordinary mains powered amp and a UPS.
4. Modeler and battery-powered FRFR speaker
Let's get the simplest option out of the way first: Continue using what you have, or get a more portable combo, and get a good mains UPS (also called a mains power bank or such). They're actually fairly affordable nowadays, and can be used for other purposes, which makes them an attractive option. They're fairly bulky and a bit on the heavy side, but acceptably so, and you won't have to make too many additional purchases.
The second-simplest option are battery-powered combos. I'm aware of five:
1. A number of plastic ~5" combos, e.g. Joyo MA-10B. Excellent choice for repair work on basses to quickly check your job, perhaps for quiet practice at home, and useless for anything else.
2. DK iB-50. It's a complete enigma to me. In theory, it has everything you might need. 10" woofer, allegedly 2-way (advertised with a 4" high frequency driver), 50 or 80 watts, depending on where you look. Has a complete set of output and inputs (even an XLR microphone input, I think I saw it even has phantom power). In practice, I never saw one in person, I can't tell you how it sounds and how useful it actually is.
3. Yamaha THR family. Plenty of hype. But there's a number of comments which mention that it's really not cut out for bass.
4. Positive Grid Spark family. Again, a lot of hype. Then I saw them constantly cropping up for sale used.
5. Roland Cube family. I only looked at them briefly. Again: A lot of hype and several comments that mention that it's useless for bass.
I think there are more options, I'm quite sure of it, but none of them satisfactory, I looked at what's available and forgot about them, so they must have been even worse than the ones above.
The third one is a modeler and a battery-powered FRFR speaker. Now, you'll note that most small FRFR speakers are not cut out for bass playing. They give you the frequency response at -3 dB, and it usually drops off quickly below 50-60 Hz. That might still be useful to you. Or not.
The fourth option is a DC-powered amp and using a USB Power Delivery power bank.
@gtirard already mentioned Phil Jones Double 4.
I'll add a few more:
1. Combo: Vox VX-50BA. 8", 50 W power, can be powered with a 19 V USB-PD power bank, just get a USB-C PD to DC 19 V cable and you're golden.
2. Head: Joyo Bantamp Badass. 50 W power, has a 24 V DC power supply, but runs well with a 19 V USB-DC cable and with a 28 V USB-DC cable.
3. Head: Quilter Interbass 45. 45 W power, has a 24 V DC power supply. I never owned one, but there are users with a positive experience here on TB.