I don't believe there is any.
If you take a taxi to the museum, you can take the 3 pm Park Connection Bus to Talkeetna Alaskan Lodge, which is about 1.5 miles from Talkeetna and has a shuttle to downtown Talkeetna. There is an early morning bus departing Egan Center at 6:30 a.m., also to the lodge. More info: alaskacoach.com/routes/anchorage-talkeetna.h…
There's also the Alaska Railroad. https:/…denali-star
You'll have to from the airport to the rail depot downtown via taxi or Uber or Lyft. Or if you don't have much luggage, you could use People Mover route 7a. Leaves the airport every hour.