Yes, snails can live in a fish bowl quite successfully, provided they're aquatic, freshwater snails. But to keep snails humanely in a fish bowl, you must carefully consider the size of your bowl, the number of snails you keep, and their adult sizes. A fish bowl may not be an ideal habitat for more than one snail.
Bowling for Snails
Fish bowls are not the best housing for most animals. They're usually far too small, ranging from 1 pint to 2 gallons. There's not enough volume for your animal's water, plus gravel, plus decorations. Bowls without gravel breed harmful bacteria, and many aquatic animals with nowhere to hide can literally die of stress. Bowls also encourage stagnant water by having very little water-to-air surface area and no room for a filter.
But There's Hope
A fish bowl can serve as adequate snail habitat. The keys are size and cleanliness. Most pet freshwater snails are so-called apple, mystery or trapdoor snails, which breathe surface air through a long tube called a siphon, so they don't need very much dissolved oxygen in the water. They do, however, need enough space to freely move and roam, to maintain normal territories and to allow their waste to dilute between bowl cleanings.
Big Enough for Rockin' Snails
Ideal minimum space for one to two adult apple snails is 5 gallons, so it may make more sense to simply invest in a small tank rather than settle for a bowl. Your snail must be able to reach the surface with her siphon, so maximum suitable water depth is about 8 inches. It's possible to keep a single snail healthy in a 1-gallon or larger bowl with live plants, gravel substrate, and weekly water changes and gravel siphoning. While it's also possible to crowd several snails into the same bowl, it won't work in the long run. Snails are fairly large when extended out of their shells. A good rule of thumb is to imagine a personal crawling space the size of a lettuce leaf for each snail. If you couldn't spread out one lettuce leaf per snail in your fish bowl without overlapping, you have too many snails. Speaking of lettuce leaves, snails cannot survive on algae and fish waste -- you must feed them a complete herbivore diet including fresh vegetables. Snails left to "clean" a fish bowl will quickly starve to death.
Death From Above
Beware of mixing fish with snails. Some fish, including goldfish, can crack snail shells and turn them into tasty meals. Other fish, like bettas, can make life miserable by attacking snails' eyes and siphons. For safety from other pets and accidental escape, give your bowl a tight-fitting mesh screen.
Sex and the Single Snail
Your snail may appreciate another snail friend, but it isn't necessary -- not even for reproduction. Most snails are hermaphrodites and can carry semen from a single encounter for their entire lives. This means your single-snail-bowl can transform virtually overnight and without warning into a many-snail-bowl. You'll have to re-home the additional snails or invest in a tank at that point.