Hi, Katie!
You will absolutely be able to get
Minnie Van service, even though you are staying at
Disney's Beach Club Villas. The Lyft app doesn't differentiate between the villas and the resort itself.
My daughter and son-in-law used the Minnie Vans exclusively during our recent stay at Copper Creek. They just had to take the short walk to the main entrance for Disney's Wilderness Lodge to catch the van, the same as you would for a taxi or Uber.
The service itself was awesome. They never waited more than a few minutes, and that was during the insanely busy Christmas week. The vans were spotless, and each driver they had was friendly and personable, and all of them had great stories or tidbits to share about their career with Disney or something about the theme parks.
Enjoy your visit, and thank you so much for your question!