It should do, formally speaking: the Mobile feat applies its difficult terrain effect "When you take the dash action"; the rogue feature lets you take the dash action as a bonus action, but you are still taking the dash action, so it still applies.
If the designers had wished to restrict the mobile feat to only applying to full actions, the language they would use would be: "When you use your action to dash," or "When you dash as an action," - a small difference in wording, but not a frivolous one.
