Platies and mollies usually don't reproduce, it's more likely that the platy has sperm stored from a different mating.
No, the bowl isn't exactly ideal. You'll have to do a lot of large/full water changes to keep ammonia down which is stressful for fish. If you do get an ammonia spike you will lose the babies and possibly mom too.
The mom platy will also have no problem eating her own young...livebearers usually do not care for the fry. They do not recognize them as being their babies and see them as food in a closed system (such as the bowl or tank). The molly will try to eat them as well.
The best thing to do would be to set up a small desktop tank and keep mom in there until she gives birth. The moment she does, move her back to the
bigger tank and keep the fry in the small one.
You can get a 1-gallon or 2-gallon glass aquarium for about $8-$10 and then you'd want some sort of lid (an actual aquarium lid for a tank this size is $5) and a simple sponge filter (around $3). If your house is cold you'll need a small heater...they vary in price depending on brand. Another option is buying a plastic Kritter Keeper...these are cheaper. You can get a decent-sized one for $5 and they come with a lid. All you'd have to do is get the sponge filter and maybe a heater. I'm not sure how large your bowl is but if it can fit a sponge filter and heater then you could use it...just be careful because the mom could technically jump out.
Another thing you could do is get a small breeding container. They are plastic tanks that go inside the main aquarium...designed to separate injured/aggressive/pregnant fish.
Obviously this won't be free (unless someone is giving away a free tank nearby) but they're really your only options if you don't want the fry to be eaten.
. To fill his spot in the tank, we bought a black lyretail molly. Only days later, we discovered our platy (who we originally named Frank until she had abies and is now called Frankie) was pregnant again. Mid-January, Frankie had about 20 little swordtail babies again. However, I moved back to school the next day and when I spoke to my sister a week later, she told me there were no babies to be found.
Make sure to pick up some food for the babies soon...they sell pellets and you can also get frozen/live foods such as 
