Sidle (verb)

1. To move stealthily or obliquely, especially in a sideways or diagonal direction.
2. To move closer to someone or something gradually and unobtrusively.

Origin:

Late 17th century: of uncertain origin.

Examples:

1. He sidled up to the bar and ordered a drink.
2. She sidled through the crowd trying to get to the front of the stage.
3. He sidled over to her and whispered in her ear.
4. The cat sidled up to the mouse and pounced.
5. She sidled closer to the edge of the cliff to get a better view.