Your question: Is it possible to use “sequentially” with the singular?
Your example: The string is wound on the bobbin sequentially from the left to the right.
There is nothing wrong with using sequentially for the reason you ask. Sequentially is defined as "forming or following a logical order or sequence" so it doesn't matter that you are writing instructions about a singular item if you are a referring to multiple steps.
However, the word is out of place in your example because the verb wound is the past particle of wind which aptly describes the ongoing action of winding the thread. Winding is a continuous circular motion, so "sequentially" does not aptly describe the action because technically there is only one ongoing step.