bucket testing is nothing but regression testing

They generally bucket test meaning some small percentage of
users, randomly chosen and see them
Bucket testing, otherwise known as A/B testing, is a
methodology for gauging the impact of different product
designs on a Web site’s metrics. For those unfamiliar, the
basic premise is to run two simultaneous versions of a
single or set of Web pages in order to measure the
difference in clicks, traffic, transactions, and more
between the two.

For Eg: you have a website selling Widgets. Right now your
site gets 100,000 visitors a month and you sell 30 widgets a
month. You would be converting 0.03% of your visitors into
customers.

So you have a web marketer come in and design you 3 new site
designs. How do you know which one to pick? Well since
you've got yourself a load balancer and a web farm, you
could install each of these new designs on a separate web
server and the load balancer will give an equal amount of
traffic to each server, or each design. Then you can sit
back and link the sales back to each particular design to
see which one is converting the best based on the numbers at
the end of the month.