Probably you are just intending to have something nice and decorative, but I must admit my first thought on reading this post was "what costume are you planning?" This is likely because we once did something similar with a small round clear faceted glass lidded dressing-table dish to make an Arkenstone for a costume (solution in that instance, small LED bike light and sellotape the lid part on securely, but I think our jar was a little bigger than your bowl, plus had the extra hight of the domed lid.)
I hope you have found a solution to your problem by now, but factors to consider when choosing your light source might include: Where is the bowl? Is it high up or low down? If low down so that people can see in, do you want your light to be intrinsically attractive (if so, look at the LED tealight options.) If high up do you want the light to basically shine through the sides/bottom of the bowl, in which case something that shines straight up like a tealight might not be so good. One possibility that occurs to me, and might even suit either scenario, is that I believe you can get individual Christmas tree ornaments that have some kind of LED lights and an on-off switch, and should be small enough for purpose. Actually I have a necklace which works this way, come to think of it, and I've definitely seen novelty light-up Xmas earrings/brooches, though possibly the lights in those would be too small/weak. Probably too late a comment to be useful, but I throw it out there in case it might be helpful now or later.
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I hope you have found a solution to your problem by now, but factors to consider when choosing your light source might include: Where is the bowl? Is it high up or low down? If low down so that people can see in, do you want your light to be intrinsically attractive (if so, look at the LED tealight options.) If high up do you want the light to basically shine through the sides/bottom of the bowl, in which case something that shines straight up like a tealight might not be so good. One possibility that occurs to me, and might even suit either scenario, is that I believe you can get individual Christmas tree ornaments that have some kind of LED lights and an on-off switch, and should be small enough for purpose. Actually I have a necklace which works this way, come to think of it, and I've definitely seen novelty light-up Xmas earrings/brooches, though possibly the lights in those would be too small/weak. Probably too late a comment to be useful, but I throw it out there in case it might be helpful now or later.