Yes there is a difference.
Bribe == gift to congress critter in exchange for a favorable outcome on a vote.
Lobby === paying a high priced spokesman whom the congress critter trusts who will explain the issue to the congress critter in such a way that the congress critter will vote in his/her favor.
Bribe == filling a brief case with $10,000.00 cash and giving it to Congress Critter to vote X on issue Y.
Lobby == giving me $10,000.00 to sit down w Congress Critter over an expensive lunch explaining why he should vote X on issue Y. Of course I put the spin I want on the issue and gain Congress critter's trust.
Consider a Lobbyist as a trusted advisor that corporations buy and Congress Critters use for free. They help break down complex issues so that Congress Critters can understand them. ;-)