Hi
please can you advise the best way to get from Milan Bergamo airport to Como then onto Bellagio . We travel in May.

bus to Milan, then train to Como
ferry to Bellagio

If you have to go through Como, the best way would be to hire a driver (look up "noleggio con conducente"/"NCC") to get you to Como and take the ferry to Bellagio (or the bus, which runs a bit more frequently but is slower) from there. You can also take a bus from the Orio al Serio (Bergamo) airport to Milan or Sesto San Giovanni and take the train to Como from there.
If you can give Como a miss, get to to Bergamo by local bus, then take the train to Varenna and the ferry to Bellagio, or the train only as far as Lecco and the bus from there. (I think the ferries from Lecco, which do exist, don't run in May, but I am not sure).

rome2rio.com (always)

Fastest way: bus to Milano Centrale railway station - train to Como San Giovanni railway station - bus to Bellagio.
As an alternative, you may go by train from Milano Centrale to Varenna, walk to the ferry pier and reach Bellagio by car and passenger ferry.

The "fastest" way would be a taxi or private transfer from BGY to Bellagio, but if the question is about public transportation this is what I would do:

(1) Taxi to the Bergamo train station (about 15 minutes). There's also a bus if you need/want to save a few euros.
(2) Train to Varenna-Esino. One departure per hour, takes about 75 minutes, easy change at Lecco.
(3) Walk to the Varenna ferry dock (about 10 minutes, all downhill). Wonderful view of the lake.
(4) Ferry to Bellagio (15 minutes)

If I was coming off an overnight journey, I'd splurge on the taxi or private transfer.

Jean has the best solution, indeed.
I didn't mention it because of the sometimes long layovers at Varenna (up to 1 hr).
But that's true for my alternative proposal too.