Remeber bowls have a lower bioload because of there shape.
WTH? Seriously - where'd you get that from? Please verify your facts properly before passing them along to folks... there's enough misinformation out there without it becoming rife here as well.
And the plants look fine to me.
OP -- If you're dead set on no heater (temps do drop at night and on cold days..) and you're keeping up the natural sun exposure, maybe use a magnetic glass scraper right before water changes so it'll flush some of the algae build up out. I'd probably be changing it a bit more frequently if there's no filter or water motion at all, and a lot of algae growing. You could also move the bowl to where it only gets a couple hours sun.