Too late for the person answering the original question, but here's how my fiancee and I will be getting from Malpensa to Bellagio.

17:00 Shuttle bus to Milano Centrale, arriving at 17:50 (5 euros);
18:00 Train to Varenna (look for those going to Sondiro or Tirano), arriving at 19:15;
19:50 Boat across the lake to Bellagio getting in at 20:10.
Sure, you could wait for the bus to Como that departs Malpensa at 18:30, and then take the 19:38 bus to Bellagio, but that gets in at 20:48, and just isn't as fun as the three modes of transportation described above

Barry: this is not as efficient an itinerary as the method described by me above, viz. train to Como via Saronno, followed by bus or ferry to Bellagio.

We have made the trip from Malpensa to Bellagio several times. The best way we found was to contact www.davideguerra.com, a driver who charged around 120E.They will eitherdrive the scenic route along the east shore ,or the faster way down the center of the peninsula. We have also rented a car which you don't need in Bellagio once you get there;parking is also a problem.The drive along either coast can be difficult especially with jet lag. Another option was to take a train to Como and walk down to the ferry dock and take a hydrofoil(www.navigazionelaghi.it). If you want to pick up or drop off a rental car, use the hydrofoil to/from Bellagio and walk a short distance to the rental car offices in Como.

GAC - I think your method is easier in terms of the number of connections, but in terms of getting to Bellagio as quickly as possible, then it depends on when you leave Malpensa. If you can leave by 16:45, then the following route is quickest:
16:45 Express to Saronno (arrive 16:53)
17:06 Saronno train to Como N.L. (arrive 17:44)
18:09 Bus to Bellagio (arrive 19:19)
However, if you can't make the 16:45 connection, as I think will be the case for us, then the route I described is the only way to get to Bellagio by 20:30 using public transportation.

Barry: I have two concerns with your itinerary: first, you may well miss your train to Varenna at 18:00. You need to allow more than one hour to travel between Malpensa Airport and Milano Centrale Station, plus enough time to purchase the train ticket (you might purchase it at the travel agency at Malpensa airport to save time). As traffic may be heavy, you simply can't assume you'll make the train at 18:00. Secondly, it takes 10 minutes on foot to walk (downhill) from the Varenna train station to the boat dock.

GAC - thanks for the advice. You're right, there is no guarantee of making the 18:00 in Milan, and if we were to miss it then we'd face a 70 minute wait for the 19:10, and then a 45 minute wait in Varenna, getting into Bellagio at 21:20.
However, taking the 17:15 express to Saronno would mean a 30 minute wait for the 18:06, followed by almost a hour's wait in Como for the 19:38 bus.
[You'd think they'd push back the departure of the 18:44 in Como by a few minutes to allow easy connection. Then your route would be a slam dunk.]
I guess it depends on how lucky we're feeling on the day. I'll post again upon return.

How about taking the 19:10 hydrofoil from Como to Bellagio?

GAC - We ended up missing the 17:00 train into Milan, which made taking the 17:15 express train the only sensible option.
[I should mention that I discussed my Malpensa-Milan-Varenna-Bellagio idea with an Italian guy on the plane, and he agreed that it would be a fun way to go.]
So we bought the express train tickets at Malpensa, forgot to validate them (no problem), and got off at Saronno.
Realizing there was only 1 minute to make our connection, we were ready to dash off the train and start running, but the distance from platform to platform (under the tunnel) was much larger in my mind, and I would say that 1 minute is actually plenty of time to make the Como train, as it only takes a few seconds.
One thing I found confusing on the train to Como is that the website always mentioned Como Nord Lago, but the actual stop does not have this name (nor do the maps on the train). Anyway, it was the last stop.
Then we had to get our bus tickets to Bellagio, which required crossing the main road to a kiosk on the other side.
As always seemed the case, the location of the ticket office for the buses was not at first obvious (Bellagio and Menaggio both being prime examples of this - the local tabacchi was the place to go).
Once that was done though, we had the pleasure of the ride to Bellagio, a truly memorable experience.
The total cost per person was only 9.5 euros (7 for the train to Como and then 2.50 or so for the bus - a real bargain).
So I definitely think we made the right call by taking your advice. This was driven home all the more when we stopped at Milano Centrale towards the end of our trip. A real zoo, and the 70c charge to use the (disgusting) toilets was robbery.
Anyway, thanks again for the knowledge GAC, and I would recommend anyone for whom cost is an issue to take the same route.

Barry: thanks so much for your posting letting us know that the trip to Bellagio via Saronno/Como was easy and went well. It's good to know that my travel advice works for fellow travellers! And think of how much you saved by NOT taking a taxi to Como or all the way to Bellagio!