Arrange racks in top third and center of oven; heat broiler. On a baking sheet, toss asparagus with oil; season with salt and pepper.
Broil asparagus on top rack, watching closely, until tender and slightly charred, 3 to 5 minutes. Reduce oven temperature to 375°.
Transfer asparagus to a large bowl. Add bacon, cheddar, Gruyère, sour cream, chives, and cream cheese; season with pepper. Wipe baking sheet clean, line with parchment, and set aside to cool.
Open crescent sheets, but don’t unroll. Gently stretch and roll each to an 18"-long rope. Using a serrated knife, cut each rope into 12 (1 ½") pieces for a total of 24.
In a small bowl, combine butter, garlic powder, and a pinch of salt.
Starting with the face, arrange 13 pieces of dough in a large circle on cooled baking sheet. For the ears, starting at the top of the head, use 9 pieces of dough to shape each ear.
Spoon a majority of dip into bunny head (it’s okay to mound it up; it will flatten as it bakes). Spoon remaining dip into ears. Brush dough with garlic butter and sprinkle with Parmesan.
Bake bunny bread on center rack until bread is golden and dip is bubbly and warmed through, 20 to 25 minutes. Let cool slightly.
Arrange chives (if using) in center of face as whiskers.