I think that the verb " To bestow " is usually used to express the action of giving a present or especially a gift, so the meaning of " To give " is general, for instance :
It is preferable to use Bestow if you want to say : I gave him money or I will give you a gift .. etc
But if you want to give something in general you say : I will give you the pen you lent to me.
Conclusion : We use the verb " To bestow " if the object is a gift or present, but the verb " To give " if the object is not a gift. This is not a rule, but it is preferable to apply it .
Thanks .