Welcome to Permies, Frank.
What kind of bay tree are you talking about? There are two North American, a Carribean, and an European tree called "Bay." You'd have to be more specific for us to say.
From what part of the world do you hail? That might give us an idea.
Generally, though, the only types of problem tree for
hugelkultur are either those that have high quantities of decay-inhibiting compound within them, like
black locust, which is possessed of an unlikely high amount of antifungal compound by weight, or those that sprout aggressively from green parts, or sometimes those that have allelopathic properties that stunt all other growth.
All of these issues, except for material that won't decay, and material that spreads its allelopathy to the surrounding soil, are temporary, as
water will dilute and biological action wash away any chemical compound.
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein