travelers and farmers, and other folks would often dress up wagons or horses, or even riders with bells -- that has been going on for ages .(sometimes for good or happy reasons, sometimes for sad-- lepers were required to carry a bell, to warn others they were approaching)

but as people migrated westward in US, and crossed Utah, and other western deserts, they often found they had to lighten the load on there wagons.. and decortive elements, like bells, were discarded.

a good trip, or hopes of a good trip, was to arrive at one destination with bells on meaning, things had never gotten so bad, that food and water held out, and you had no need to lighten the load...

so while the bells are old, and common in both UK and many part of europe, to do something with bell's on is an american idiom for doing something, not just successfully, but with ease.