All of this is guessing but...
Depending on what the WH
has to spend out of its 100k it may be covered. Here is my guess as to how it breaks down.
Air Transportation - Planes are assigned to the Air Force as military transport. So, when he uses those planes to fly, he is acting as Commander in Chief. Air Force foots the bill. Since the US Secret Service deems it necessary for the president's safety they may pay the Air Force to transport the Presidential Motorcade.
Ground Transportaton - These are Secret Service vehicles...their responsibility.
Press on Air Force 1 - They don't fly for free. And doesn't the White House charter planes for the rest of the press traveling with the President? I wouldn't be suprised if the fares they pay are way above the cost of a seat on a commercial flight to the same destination.
Hotels - Only the actual suite the President and his immedate staff stay in...All other suites would come out of the budgets for their respective agencies (Secret Service, Air Force, etc.) Plus many times the President is attending a summit or a function of another state, which means lodging is pretty much covered for the President.
On Site Security - Again comes from Secret Service taking lead along with local/state law enforcement.
So while the White House may have 100k for travel, as you can see, the travel support
costs are probably covered under someone else's budget.
Always wonderers if this "last and final boarding call" is in fact THE last and final boarding call.