Blackberry bush trimmings and where/how to dispose of them?

I received bought a house here in WSea, and I inherited a massive blackberry bush/vine that has taken over about 40’X60’ of my rear property line. Survey shows it’s an easement for the city, but neighbors have sheds and such on theirs. I just have blackberries. Now my issue is: I’m trimming them back and making a path to my property from the rear(also a road, not an alley) but the “yard waste” container provided by the city is not large enough. I don’t want to cut them and leave a mess on the road. I also don’t want to have to cut them in stages (weekly waits for the waste disposal). I don’t think we can do a burn right now, so I’m out of ideas. Any help or direction would be appreciated. Also, this bush/vine has been supplying the neighborhood for years with berries, so I’m NOT removing it, just trimming. And if you want some berries, DM and I’ll be happy to provide you the street number!