What you have described is not possible. Jira does not support the concept of a Work Item as having two parents, one of which is the parent of its parent.

In the scenario you have described, the Bug Issue type would be the grand-child of the Epic Issue type and so cannot simultaneously be a child to the Epic. The only way to create such a hierarchy would be to create separate Issue type, say, called Bug#2 for example, and make it a child of the Epic only, with no relationship to the Story, so the structure would be:

Level 1 - Epic
Level 2 - Bug#2
Level 2 - Story
Level 3 - Bug

However, that would be totally pointless, as it would defeat the purpose of having the Story as being the child to the Epic, as it would be duplicating the function that is now being filled by Bug#2

I recommend that you spend a bit more time reading about Jira's default issue types and the hierarchies they can be arranged into.