The president’s security budget is classified so we can t know all the details. Secret Service faces massive bill for protecting Trump - POLITICO
That said, there is good reason to believe this president’s security budget will dwarf that of recent predecessors. As you note, he travels constantly to Mar-a-Lago. His wife maintains a full time residence in New York. His children travel abroad for business.
Some portion of this cost is simply pushed off onto the state’s and municipalities where he travels. Melania costs the New York City police department millions. It’s uncertain whether they will be repaid. Perhaps Broward County Florida has the same issue when the president visits. Congress would have to appropriate money to repay these costs. It wouldn’t come out of the Secret Service budget.
The Secret Service budget largely goes to “operations” without much detail. It requested about $2.15 billion total for 2017 with $1.77 billion for for operations and support. Pdf of 2017 Secret Service budget request: https://www.dhs.gov/sites/default/files/publications/FY2017BIB.pdf
This operations budget covers all the Secret Service missions: protecting the president’s family, protecting foreign dignitaries to the U.S., protecting foreign embassies, safeguarding the White House complex (which includes the Treasury building, Eisenhower executive office building, and the Office of Management and Budget too), and investigating counterfeiting and financial crimes. If the Presidential protective detail starts to spend too much, the Secret Service director can take money from these other programs. Since he reports to the president, I’m betting he’d do that instead of telling the president, “You’re on your own!”
There is one budget-saving measure for the protective detail: Secret Service agents’ salaries are capped. Congress Looks to Ensure Secret Service Agents Receive Earned Overtime Pay - Government Executive
In theory, if the overtime for presidential protection detail gets too high, agents having to work without overtime pay should limit the damage. It doesn’t work out that way. When agents reach the cap, many will request unpaid leave and stop working altogether. If the unpaid leave is denied, they may just quit. Secret Service agents are in demand for corporate security jobs, other jobs in federal agencies, military contractors, etc. They will find good work. The Secret Service is currently understaffed and it has trouble recruiting due to the stringent hiring standards, the low morale, and the disappointing pay.