You don't need a lot of bandwidth, but you do need a solid connection. We recommend uplink bandwidth of 1Mbps to support a session with 4 musicians. You definitely want to connect via an Ethernet cable to your home router, as WiFi routers tend to bog down due to packet rate, not bandwidth. And cable and fiber broadband works best. DSL typically has too much packet loss, and satellite too much latency.
JamKazam streams all musicians audio to each other and mixes the streams from other musicians with each musician's own stream back into his/her headphones. So you hear everyone, including yourself, mixed together. As long as latency is reasonably low, it feels like you're playing with others in the same room with your eyes closed. If you check the videos of various bands on the JamKazam YouTube channel, that's what they were all doing.
If you look at university research papers that have studied this domain, and if you look at first-hand experience of watching musicians play with different amounts of latency, they can tolerate just a little latency. From research and experience, we'd say 0 to 20ms of one-way latency between musicians yields a tight session we'd label as "green". This is like playing in the same room. In the 20ms to about 35ms range, you start really feeling/hearing the latency more, but it's still manageable and can yield a fun and productive session. Somewhere up in the 35-40ms range and greater, it gets increasingly sloppy until it's just not fun or worth it . These are general rules of thumb. It also depends on the tempo and the level of precision required. And some musicians are more or less sensitive to it. But if you consider the speed of sound, playing with 20ms of latency is like playing while sitting 20 feet away from someone on a stage or in a room.