It will not be very quick. They have a lot going on at present.
And they like to break down the distribution to a number of smaller units so there is a fair bit of work to be done.
When its done, it will spend a few days in unstable then, hopefully, migrate into Testing. It will not migrate to Bullseye so unless you are using Testing as your distro of choice, you will not see it for close to two years.
Its possible, but quite unlikely that L2.2 will make it to backports, they have some pretty strict rules about what goes into backports and just normal progress probably won't qualify.
On the other hand, once L2.2 is in Testing, distros like Ubuntu that release far more often will pick it up.
Davo