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Not specific to any one president or party but using Trump as the most recent example.

Trump has been on the road for weeks campaigning for the Republican Party midterm elections. I've searched around and see some references that the political party should pay for these expenses, but the president's mobility costs millions and millions of dollars each day. Secret Service, Air Force One, limos, local police, I'd think a few weeks on the road would run the party dry pretty quickly if they had to foot the bill.

If the American people are footing at least part of the bill for this, why is it allowed?

The way it often works is that a President doesn't travel explicitly for campaign purposes.

The trip is often billed as official business. In other words, the trip would supposedly occur regardless of any political campaign or cause.

The thinking then goes, "but hey, what the hell, while I'm there, let's do a fund-raiser with George Clooney" or "... a rally for Senator Ted Cruz".

There are variations of this paradigm, but the basic concept is generally the same.

This allows the taxpayers to "legitimately" pay for all expenses relating to the President's trip. (If the trip were presented exclusively for campaign purposes, the opposition party, government watchdog groups, and others would be crying foul and demanding reimbursement of taxpayer funds.)

For a more detailed analysis of these Presidential trips (along with examples), see this article:

• 
  Trump's travel expenses test boundaries of policy and politics ~ Chicago Tribune

A sitting President gets some slack in campaigning for re-election because they do still require a security detail and transportation. Both sides have figured out that, as long as it's not explicitly a campaign event, they can get taxpayers to foot some or all of the bill.

As noted during Obama campaigning for Clinton

In the most recently available figures, the cost of operating Air Force One averages approximately S180,118 per hour, according to the Air Force. This figure includes fuel, food, repairs, and basic maintenance.

"As is the standard practice, the campaign will cover its portion of the costs," a Clinton aide told ABC News.

But while relevant political organizations may be on the hook for paying part of the costs associated with the plane’s operation, there are additional security costs associated with presidential travel that do fall to the taxpayers.

Basically, Obama went campaigning for Clinton, who rode along with her entourage. Obama's travel entourage were taxpayer funded, while Clinton's campaign had to reimburse for riding along.

In the case of political figures flying aboard Air Force One, as was the case today with Hillary Clinton and several of her campaign aides who also traveled with her, Painter said they did not get a free ride.

There’s a formula by which they are charged for their flight comparable to the cost of a commercial first class ticket, he said.