The situation is just as stated in the title: my opponent controls Eidolon of Blossoms:
Whenever Eidolon of Blossoms or another enchantment enters the battlefield under your control, draw a card.
I target the Eidolon of Blossoms with Hypnotic Siren, gaining control of it:
Bestow 5UU (If you cast this card for its bestow cost, it's an Aura spell with enchant creature. It becomes a creature again if it's not attached to a creature.)
You control enchanted creature.
Enchanted creature gets +1/+1 and has flying.
Do I draw a card for Hypnotic Siren coming into play? My instinct says yes, because of rules 603.6b and 603.6d:
603.6b Continuous effects that modify characteristics of a permanent do so the moment the permanent is on the battlefield (and not before then). The permanent is never on the battlefield with its unmodified characteristics.
603.6d Normally, objects that exist immediately after an event are checked to see if the event matched any trigger conditions. Continuous effects that exist at that time are used to determine what the trigger conditions are and what the objects involved in the event look like.
but I'm not 100% certain. (I had it ruled the other way at FNM this evening; at the time I agreed with the ruling, but now I'm less sure.)