What would be considered a religious experience in Buddhism in the same way,for example, Moses' experience with the burning bush of God? Would it be the Buddha's enlightenment itself or a bodhisattva's interaction with Buddha?
Examples of religious experiences in Buddhism:
- traveling with one's mind to other worlds
- speaking with supernatural beings, like Devas
- remembering past lives
- witnessing an enlightened person flying, being in multiple places at once
- having an enlightened master read your mind and respond directly to your thoughts
It would be unwise to 'trim down' Buddhism to fit into "religious experience" and/or associating direct equivalents.
When you mention "Moses' experience with the bush of God", you are implying a God vs Man hierarchy/relationship exist in Buddhism. However, such hierarchy does not apply in the teachings of the Buddha, nor exist between the people at the times of the Buddha, the Dharma, nor the Sangha.
You can find here some useful quotes on this topic by Ajaan Fuang:
"Don't be amazed by people with visions. Visions are nothing else but dreams. There are true ones and false ones. You can't really trust them."
"There are true visions and false visions. So whenever you see one, just sit still and watch it. Don't get pulled into following it."
"You should watch visions the same way you watch TV: Just watch it, without getting pulled inside the tube."