Nothing […] amused Lear more than the failure of some people to appreciate the utter absence of sense in his nonsense. He used to relate that some one once wrote to him to say that he had marched various botanical and other works without finding any allusion to a “Bong-tree.” Where, his correspondent, asked, did the “Bong-tree” grow?
[Evelyn Baring, “Introduction.” Queery Leary Nonsense. A Lear Nonsense Book. Edited by Lady Strachey. London: Mills & Boon, 1911.]
The question is a recurrent one, and I myself have sometimes been asked it, why the Bong-tree? The problem of the Bong-tree is an early one if the producer of The Owl and the Pussy Cat and Other Nonsense Songs, Illustrated by Lord Ralph Kerr (London: Cundall and Co., 1872), which you can see in facsimile in our Picture gallery, felt the need to replace it with a more appetizing and less nonsensical “Jam-tree”.
Vivien Noakes, in her definitive edition (Edward Lear. The Complete Verse and Other Nonsense. London: Penguin, 2001: 507) presents the modern interpretation:
The coach-road along which Lear would have travelled between Liverpool and Knowsley, passes through the village of Knotty Ash, said to have taken its name from a gnarled ash tree which once stood outside the public house beside a group of cottages called ‘The Little Bongs’. The tree was known locally as ‘the ash tree at Little Bongs’, and may have been the inspiration for Lear’s Bong tree.
Noakes prudently adds that “on the other hand, he may just have liked the sound of the word”, and in fact manuscripts at the Houghton Library and Pierpont Morgan Library contain variants (“Phloss tree” and “Palm tree” respectively).
Another influence on the final choice of the name which I have never heard mentioned might be the “Bo-tree”, or Indian fig tree, said to be the tree under which the Buddha became enlightened (Ficus religiosa, family Moraceae). On its eastern side is “the immovable spot on which all The Buddhas have planted themselves! This is the place for destroying passion’s net!”. While Siddartha is sitting there he is attacked by the god Mâra, but his perfection protects him, and the evil god is defeated (Buddhism in Translations. Passages Selected from the Buddhist Sacred Books and Translated from the Original Pâli into English by Henry Clarke Warren. Harvard University Press, 1896. § 8: The Attainment of Buddhaship). Just after attaining buddhaship “the Blessed One sat cross-legged for seven days together at the foot of the Bo-tree experiencing the bliss of emancipation” (§ 9: First Events after the Attainment of Buddhaship).
The quest of the owl and the pussy-cat is more earthly, of course, but it also leads to bliss, and the rhythm of the poem, with its long, repeated sounds at the end of each stanza clearly gives it some sort of ecstatic quality.