My reading of the rules is that you can't: Paying the bestow cost doesn't make the card into a (non-creature) Aura until after it's on the stack, and Steel Golem's restriction doesn't let you put a creature spell on the stack.
In general the ordering of steps in casting a spell is:
- Choose a spell to play and place it on the stack.
- Choose modes and targets.
- Choose which costs to pay and pay them.
When applied to a Bestow spell, these become:
- Place the bestow creature on the stack.
- (No modes or targets to choose yet, since it's a creature spell).
- Choose to pay the bestow cost.
- The spell stops being a creature and becomes an Aura (702.102a).
- The spell's controller chooses a target (702.102b).
But if "you can't cast creature spells", then you can't complete step 1, since your Hopeful Eidolon is still a creature. And (per 601.2) "If, at any point during the casting of a spell, a player is unable to comply with any of the steps listed below, the casting of the spell is illegal".
(The converse situation seems to arise with Aurelia's Fury, where a Bestow card is playable because it's not a noncreature card until after the Bestow cost is payed.)
Does this sound correct or am I missing something?