The smallest I would go is the Cube Street EX. It's about the biggest option I think is practical for walking and hand carrying. It weighs about 16lbs.
Roland - CUBE Street EX | Battery-Powered Stereo Amplifier
Cube Street EX has a pair of 8" woofers and claimed power is 25W x 2. In reality I think it performs about like about a 13W amp. Headroom is limited so some sort of battery powered multi-processor with built in compression and a HPF would be a good add on. I believe
@brianrost uses a Zoom B3 rigged up with a battery or some sort of power pack.
You can run the Cube Street EX on Eneloop rechargeable batteries, however my understanding is it makes more power if you buy the pricey Roland power pack. Case and battery packs shown on this page:
Traynor makes a bigger and more powerful battery powered bass amp. It's about twice as heavy as the Cube Street EX at 32lbs, but has a 12" woofer and makes 80W on the built-in battery. I think this is a legit 80W.
Traynor BassMaster 12 Mobile: a full-sized, battery-powered bass amplifier with a 12 speaker. Offering over six hours of performance on a single charge, and weighing just 32 pounds.
traynoramps.com
While I would appreciate the extra headroom of the Traynor, I think 32lbs is too big to carry. I would consider something this big if it made sense to put it on a cart.
Not that I will ever use it, but I went the power bank route and bought a Jackery 300 which weighs about 7lbs:
The Jackery Explorer 300 is the ideal portable power station for short camping trips, off-grid living, and for powering small appliances when power outages.
www.jackery.com
I have a GK 700RB/112 combo. This amp makes 225W into the internal 12" woofer. The amp is too big and heavy to carry, but it's a tilt back design and has a telescoping handle, so it rolls around like airport luggage. It would be easy enough to strap the Jackery to the top of the amp. The amp does make a low level hum on the Jackery, but I don't think it would be a problem for most busking situations. In regards to tone and headroom, I don't notice any difference between the amp on wall voltage or the Jackery.