Once you have the frame (bubbleframe here) you can use:
Lua Code:
for i = 1, select("#", bubbleframe:GetRegions()) do
local region = select(i, bubbleframe:GetRegions())
if region:GetObjectType() == "FontString" then
region:SetShadowOffset(2, -2)
end
end
Personally I can't figure out when/why the system will use protected chat bubble frames or not.