Lake Como and the Dolomites in one week

Yes u can but not easily. Both areas are blockbusters beauties that should not br rushed by public transit. I had a car rental and could barely fit both in. I suggest u rent a car or decide on one area.
Sure with more time u could do all on public transit.

The towns of Como on the east side and Varenna (much smaller and more scenic) on the west side of Lake Como are both easily reached by train from Milan. Varenna is one hour away from Milan.

You can reach Bolzano by train north from Verona (heading to Innsbruck in Austria). There is excellent bus service by SAD bus (Sud Tirol Autodienst) from Bolzano to Castelrotto, and from there you can reach Alpe di Siusi by SAD bus, or by cablecar from Siusi. We rode the bus as our visit was before the cablecar was in place. You can also reach Alpe di Siusi by cablecar from villages in Val Gardena, such as Ortesei. This works well if you want to stay in a village and head up to Alpe I’d Siusi to hike or mountain bike.

On four visits to the Dolomites we used the bus twice and rented a car twice. A car gives you more flexibility to move around for sightseeing, but if you simply want to base somewhere and hike, the SAD buses work very well.

Absolutely you can! We visit the Val Gardena every year and never by car. Train to Bolzano by way of Milano and Verona, then bus to Castelrotto or all the way to the Val Gardena. Give yourselves at least three nights. Four is better. 😉

Editing to say you can take a bus up to the Alpe from Castelrotto, but the gondola lift is more fun.

If you drive, you could consider driving from Varenna to Sondrio to Bormio to Stelvio Pass and descend toward Meran and Bolzano. Glorious drive. Of course check road conditions.