I read somewhere that "every garden uses energy". I suppose that is true but certainly a bush garden would use much less than most. There is no reason to use fertilisers, pesticides or chemicals of any sort in a bush garden.
In fact the weeding, from a bush garden, produces enough compost that enables the vegetable garden to function without the use of fertilisers or chemicals there. So, in a way, a bush garden uses negative energy.
The only energy, that I can think of, is the mowing done as part of maintaining a bush garden. I mow my bush garden about once every five years. In fact I do a fifth of it every year but a different fifth. I would use a couple of litres of petrol a year carrying out this chore. I like to think that this is less than the fuel I save by growing my own vegetables without fertilisers or chemicals. However I don't really know the answer to that.
This summer I am going to try using hedge shears instead of the mower. If this works ok then I will have reduced my energy use to zero. That is not counting my energy of course.