Instead of using the AE name.. try using the AE IP address.
SMB does not like some apple setups. I find it more reliable if you use IP instead.
Tesserax suggested.
Windows will see your AirPort Disk as: \\<AirPort base station name>\<AirPort Disk share name>
What I would try is replacing <AirPort base station name> with 10.0.1.1 (or whatever ip it is).
Also note that IP must be static.. so if the AE is bridged be sure to set static IP via dhcp in the router that runs the network..
You can also use this method to keep the AE on static IP.. I find this works well.
https://discussions.apple.com/thread/5981989?answerId=25135547022#25135547022&ac_cid=tw123456#
Fixing this fixes the need for workgroup or domain problems..
The disk share name should also be short no spaces pure alphanumeric.. the default is data which is fine.
It can be also help if you used a windows computer to create a separate shared folder in the AE disk.. again this helps keep permissions the right way around.
The disk access password should normally be set to the same as the admin access to the AE.. don't forget to change it if you actually set a different disk password.
Otherwise sorry as Tesserax says .. apple builds for apple and they don't really care much if windows or other stuff works or not.