If you use the access path do you have to use this part of their drive to put the bin by the road?
Is there an other route?
Have you checked your title deeds regarding whether you have an easement?
You can get a copy of your title deeds from the Land Registry.
This can be done online but I think you need an account. A local solicitors who do conveyancing can do it cheaply.
The title deeds will show if you have an easement over your neighbours land to use it to take your bins.
If it does not show an easement you have no right to continue doing it despite the fact you have done so for a number of years.
The reason is that it is not the only route you can use.