i wouldnt keep them in a bowl, unless it was a big one. i had one in my 10, then 20 gallon community tank and he loved it.
they have a lot of personality, though i suppose it depends on the individual fish. mine(who just died today

) liked to be "petted", ate out of my hand, and was as much of a beggar as my oscar. he was always up and about, especially when i came close to the tank.
they need a heater(78-80*), a filter, and clean water. yours probably did better in the dirty water because he was used to it. when fish in high nitrate water for a long time get a water change, they get really stressed, could get shocked and even sick from the stress or die. people encourage acclimating to clean water for tanks that have been miserably maintained.
bettas like live plants, wont ever eat them. ive found(and so have others) that they like to sleep on "beds" near the surface.. like a driftwood stump or a wide leaved plant. they like to be near the surface so they can take a breath easily. they dont do well with fast water movement or heavy current, and come from generally still water environments in the wild.
if you have them in a larger tank, like a 10 gallon(in comparison to their plastic cups and bowls).. they like to have a sheltered area, or a decently planted area to chill in when theyre not swimming all around and exploring. i think a 5 gallon is a perfect size for them, though they will still use all the space in a 10.
they can live 4-5 years if well taken care of, and are usually about a year old when you get them at a LFS. sometimes younger, sometimes older obviously.
id say get one! they have the most personality of any little fish that ive ever had.
when you are picking one out, look for illness as always, see how responsive they are, etc. you want to pick out a feisty one.