I visited Skwerl in Orlando last Winter. I was climbing something small for him, and watching as he assisted his ground guys in moving a big block of wood up onto a trailer using his bucket. I'd never used a bucket before, so I didn't know if this was normal or not.
He shared with me that his bucket truck was purchased from a municipality. The jib itself had a winch attached to it, alongside the actual bucket. Rocky let me know that they don't sell these to the arborist community for fear of what we'll do to them. In the municipality, the biggest thing they might lift is a pole. In tree work, the biggest thing we might lift is..... well, at this point you can see why they don't market these trucks to us.
I would listen to the guys here who say DO NOT rig off your bucket. It's not built for that.
I would also listen to the guys who say you should get comfortable using slings. If you think they would slow things down, you clearly don't understand the use of slings. I rig and lower everything from up in the tree, climbing, so for you to do the same thing from a bucket should technically be easier. Usually I rig without a sling, or slings, but in the hairy spots, slings make that sort of work possible.
I recommend having a non-locking stainless steel slideline biner on each of your web slings and nothing on your rated endless sling(s), to which you attach your 50 Kn steel biners and blocks, as needed, for the heftier rigging exercises. Heed Mike's advice for selecting a single point from which to lower and do the general area there before resetting your placement.
You can tie your own slings, or buy them pre-sewn. Tubular webbing is cheap. The slideline biners are 12 or 15 bucks. Have a minimum of two on you. For really active rigging, I like six. Try out various lengths to determine what you like. They don't take up much space. They really amp up your versatility and can make the job much safer, and believe us, faster. You'll warm up to them pretty quickly. Get spliced eyes in both ends of your rigging line to get out of the rut of the tie and untie and tie and untie and tie.... and of using just the one single end of the rigging rope all the time. These little nuances can make a big difference in the efficiency of your rigging.