I never take a large sharps bin with me anywhere - it lives in my study and stays there until it is full.
When I go away, I take any pot or bottle with a lid. Depending on how long I go away, this could be a plastic water bottle (for a fortnight) or a test strip tub (overnight) or a small shampoo bottle like Body Shop used to have (for a weekend).
And then, as others have said, I decant into my sharps bin when I get home. It is one of those chores like emptying your laundry when you get home.