Two bins, a box and a bag here.
It doesn't take us any time to sort waste; we have a little plastic chest of drawers by the bin in the kitchen; there's a drawer for cans, one for glass, one for paper, one for tetra packs and so on. We just put the item in the right drawer: sorted.
In rural York-ish, Ryedale Council don't collect recycling except garden waste, paper, glass and cans. Most of our rubbish is plastic: milk bottles and food packaging. We keep that to a minimum, unwrapping stuff in the shop and so on, but there's always some.
As we have a wood-burning stove, we simply burn it. Open all the vents and burn it good and hot and it's gone in minutes, heats the house or the hot water, produces almost no ash and no smell.
We also compost almost all our garden waste, or burn it. Food? We never throw food away. If we aren't going to eat it, we don't cook it. Or we freeze leftovers and eat them later. In the last resort, the dog eats it. For a while, we had chickens, and they'll eat anything.
As a result, it's quite rare that we ever actually use our wheelie bins. When we put an almost-empty one out, often the bin men just assume it IS empty and don't tip it out. Or our neighbours fill it for us!