score:2
Rome2Rio suggests the following route:
Bolzano/Bozen - Fortezza/Franzensfeste (train, 43min, hourly)
Fortezza/Franzensfeste - Dobbiaco-Stazione (train, 1h 15min, every 30 minutes)
Dobbiaco-Stazione - Misurina-Genzianella (bus 444, 23 min, every 3 hours)9-33€ / 3h 40 min
An alternative would be to go to Cortina d'Ampezzo and take the bus from there.
Upvote:2
Trenitalia (main italian train player) changed their website again and looks like it's impossible to find any cheap solution. (they force you to use high speed high priced trains)
It will take about 6 hours and 56 € to get near Misurina lake.
Your travel plan is:
Bolzano Bozen -to- Verona Porta Nuova
Verona Porta Nuova -to- Venezia Mestre (do not arrive to Venezia, this is the station before)
Venezia Mestre -to- Cortina d'Ampezzo
From Cortina d'Ampezzo you may catch a local bus to Misurina.