A TSB is not the same thing as a recall. After production of a vehicle, if enough cars show evidence of a specific problem, the manufacturer will release a TSB to service departments to let them know this is a known problem and what the fix is.
When the problem becomes a safety issue, then the TSB may result in a recall. If there is a recall, the work will be done as warranty-covered work, even if the vehicle is no longer under the initial warranty. However, not all TSBs result in recalls, and those that don't would not be covered under warranty.
Occasionally the US government has forced recalls on manufacturers even though the manufacturer claims there is no safety issue.
Sometimes there is some allowance for "goowill" work.
If it is a bad part, maybe the part will get covered if you puick up the labor.
It is all up to how much the TSB issue is related to the problem, the dealers attitude, your attitude, ect.