Heat the butter in a thick-bottomed saucepan over medium-high heat. Add the onions and bay leaf and cook, stirring constantly, until the onions become soft and clear.
Reduce heat to medium and add the butternut squash. Cook this mixture, stirring occasionally, until the squash begins to soften.
Lower the heat to low and add the shrimp, salt, cayenne, and white pepper. Cook, stirring occasionally, until the shrimp turn pink.
Add the shrimp stock and cook, stirring occasionally, for 6-8 minutes. If the mixture begins to stick to the pan, scrape it with a spoon and continue cooking. This will intensify the flavor of the bisque.
Remove bay leaf and discard. Transfer the squash/shrimp mixture to a food processor and puree with about 1/4 cup of the cream.
Return the puree to a saucepan and add the cream. Whisk until thoroughly blended. Bring to a boil, then reduce heat to a simmer for a few minutes. Adjust seasonings and serve in pre-warmed bowls.