There are various kinds of honeysuckle. Do you know which yours is?
I don't know why yours isn't blooming but when I have a plant that should be blooming... it's the right time of year, it's old enough, looks healthy, but just isn't blooming, banana water almost always makes it bloom. Pureรฉ a banana peel or whole banana if you feel luxurious and dilute that in your watering can, water the soil all around the plant with the banana water. If you try it, please let me know your results.