Some crazy advice here, to say the least.
You have 3 realistic options, trains, car hire or taxi.
Trains from Bergamo towards Riva are simple to manage, cheap and relatively quick. Get an airport bus or taxi from Bergamo Airport to train station (beware, taxis can be hard to find if you're arriving during siesta time. Then take a local train from Bergamo to Milan, an express train from Milan to Verona & another express from Verona to Rovereto (on the main Verona-Trento line). Rovereto is c.15km from Riva. You can get a local bus or a taxi (about €35) from Rovereto to Riva.
I would recommend Car Hire if you are perplexed by the train connections. Otherwise use
www.trenitalia.it to plan your journey. If taking a car, drive "the long way" from Bergamo to Milan/Venice motorway, then somewhere around Verona take the motorway towards Trento. Exit at Mori/Rovereto and proceed towards Riva (15km on a country road).
Do not take the lakeside road from Garda/Desenzano. This is very slow, busy, dangerous road (far worse than an average Irish road) and littered with tunnels. The road on the other side of the lake via Limone etc is worse still, and is also particularly dangerous as some of the tunnels are not high enough to properly accomodate trucks, who have to go into the middle of the road to get through. You might well go around a bend only to see a truck in the middle of the road coming straight at you.
Some families we met in Riva last year had taken taxis from Bergamo for the guts of €200 (booked in advance). They thought it was worth it, as they were in Riva within a few hours of arriving in Bergamo and they did not have any of the hassle of train/bus connections or car hire.
Bus might be an option, but the local buses in that part of Italy are very slow. If there are more than 2 of you, taxi would be far easier and quicker.
Do not under any circumstances consider taking the ferry from Desenzano/Sirmione. Desenzano & Sirmione are 4 or 5 hours on the ferry from Riva. This would be a tortuous journey after successive plane and train rides.