We've all been "there," trying to make an exit and assessing the best way to do that. Whether it's professional, personal, conversational, or metaphorical — as in needing to make or keep a boundary. The reason is irrelevant really. This is about delicately, skillfully, and politely breaking away. Sometimes we just need to step back for some space to protect our time for any number of reasons. In the give-and-take of life, we give by participating (fully present for the needs of the group and for others, or our commitments) and we take by not participating (fully present for our own needs or commitments to ourselves) and both are part of the balance when living fully. "Slipping out" is figuratively about honoring one's own boundaries, and is literally about leaving the party when it's time.
It's not a grand ceremonious fanfare of a goodbye, it's a quiet and clean, unnoticeable, and non-disruptive departure. The party is in full swing and should continue that way, we're just going to slip out deftly and respectfully.
"Slipping out" unwinds, telling a story. In my mind's eye, the narrator or protagonist could be Audrey Hepburn or Carry Grant, they are in a crowded lounge or bar in a 1960s movie. The environment is jovial and people are in small groups having conversations gesticulating, and reveling. The narrator is trying to leave without making a fuss or being detected, as to avoid entanglement, and being drawn back in. There are waiters carrying trays, and people who might try to have a word for any number of reasons, but the mission of the moment is to slip out. It's a sticky task, and plotting an exit politely is a dance that involves thoughtful navigation toward the exit.
The two bar phrases between lyrical sections are thinking moments. Surveying the space, before taking the next steps.
The idea of "letting down my hair" and "rolling down my sleeves" is a nod to work. The phrase, "rolling up sleeves," is used to talk about getting ready for work, and putting up hair is about being pulled together and ready for work, be it social, professional, or metaphorical. Those lines are about relaxing and being natural. Off duty.
The song ends with a celebration, the mission successfully accomplished. "Slipping Out" is designed to be fun and playful whilst telling the story of personal freedom and agency over time and commitments.