At least in my state, you can't. The bill is officially linked to the legislator who introduced it, not the person who wrote the text.
When a bill is introduced it bears the name of the legislator who introduced it. There is no mention of the staff that wrote the text (a short example bill is below). In Kansas this work is done by the Revisor of Statute and they won't tell you which particular staff member worked on a bill. The closest you can get is seeing which staff typically work in which subject areas.
Why isn't this information public? The legislator is accountable for the content, not the staff. The staff who write the bill don't determine what the policy goals are or how to accomplish it. They write the bill the legislator wants, and they provide some technical legal assistance to help it gel with other statutes.
My colleagues in other states have described similar things. For example, the Nebraska Revisor of Statutes and the Missouri Revisor of Statutes.