Using a colander set over a bowl, strain the oysters, reserving juice.
In a medium skillet over medium-high heat, add bacon, and cook until crispy. Set aside bacon, and reserve 3 Tbsp. rendered bacon fat. Crumble bacon when cool. Reserve skillet.
In a large bowl, combine fennel, 1/2 tsp. salt, 1/4 tsp. ground black pepper. In same skillet over medium heat, add 1 Tbsp. bacon fat. Add fennel, and cook, stirring, until caramelized. Set aside, and reserve skillet.
In same skillet over medium-high heat, add remaining 2 Tbsp. bacon fat. Add mushrooms, and cook until crispy, 3 to 4 minutes; reduce the heat if pan begins to smoke. Add 1/8 tsp. salt and 1/8 tsp. pepper, and using a slotted spoon, transfer them to a paper towel-lined plate. Return skillet to the burner.
In same skillet over medium heat, add shallot, and cook until tender. If mixture looks dry, add 1 to 2 Tbsp. olive oil. Add oyster liquor, and reduce by half. Add cream, and reduce by half, 6 to 8 minutes. (The cream should just coat the back of a wooden spoon.)
Add potatoes, reserved fennel, bacon, thyme, parsley, fennel fronds, and oysters to the pan. Cook over medium heat until the edges of oysters just begin to curl. Add mushrooms, and remaining 1/4 tsp. salt and 1/4 tsp. pepper. Divide sauce between 4 bowls and serve oyster mixture on sliced grilled ciabatta.