I have a Jackery 300 which is pure sine. I tried my GK 700RB and it does have a low level hum on the Jackery.
I believe this is because the output on the jacker is only Hot and Return...no ground.
Amps use the ground connection to reduce hum. There may be a way to bodge some sort of connection between the chassis of the Jackery and amp, but I don't know if it can be done safely.
The amp I would suggest is the Roland Cube Street EX. It runs off AAs and I recommend getting some Eneloops and a charger. The amp does not have a built in charger.
The Cube Street EX is rated at 25W x 2 and has two 8" woofers. I believe actual power is closer to 12.5W (total). IMHO this amp is still small and light enough to work well for camp fire jams, and I think it will give you a bit of headroom when playing with a couple of drunks thrashing nice dreadnaughts. It will sound more like a PA cab than a bass amp. For the record, this would be my choice.
Roland also makes some smaller amps. The regular Cube Street is rated 2.5W x 2. I have actually played my Tacoma Thunderchief ABG through this model and it seemed about as loud as the gass. Also, it farted out super easily if I did not play with restraint.
Roland recently discontinued the Bass Cube RX with is rated 2.5W x 2 and has four 4" speakers. Years ago I tried one in a store and was totally unimpressed with the volume it could produce, but YMMV. This one will sound more like a bass amp and people seem to like its built-in rhythm module. I don't think this amp will give you much if any headroom against a couple of drunks with dreadnaughts.
The Bass Cube RX has been replaced by Boss Dual Cube Bass LX. This is rated 5W x 2 and has two 5" speakers. So it the amp makes +3dB more power, but less speakers could mean less efficiency...meaning it may produce about the same volume as the Bass Cube RX.
Roland makes a BA-330 amp that I think has a bit more headroom than the Cube Street EX, despite making less power. This amp also sounds more like a PA than a bass amp, and it is rated for 15W x 2 and has four 6.5" woofers. It's approximately twice the size and weight of the Cube Street EX...so I think it's a bit too bulky and heavy for the campfire scene.