Answer: It is usually better to root tip cuttings from woody plants in a soil mix rather than water. You would need to use a soil mix that drains well and keep it just slightly moist. A mixture of one half milled spagnum peat moss and the other half clean coarse sand or perlite would work, for example, or you could use a soil-less potting mix formulated for container plants. You might also need a rooting hormone to treat the cut end. These come in powder or liquid form. Read and follow the label directions for how to use that. Here are more detailed directions on how to root tip cuttings.
Since Laurus nobilis is a container plant for you (it is not hardy outside in NY or in DC area), do not plant it out in the garden, just keep it in a pot year round so you can bring it inside in winter. I should also mention that this is a difficult plant to root. Good luck with your project!
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