Can a regular citizen get a bill written so it can be passed into law?

Answer 1

Yes a regular citizen can write a bill and get it passed in to law. How happens will depend on what jurisdiction would pass the law.
On the federal level there is no direct manner for a citizen to introduce a bill and have it become law. However, a citizen could write a bill and take it to their senator or representative and have them introduce the bill.
On the state and local level you can use the above process except the bill would be given to the appropriate legislator.
Some states and localities have a proposition process where a person can write a bill, gather some number of signatures on a petition and then the proposition is placed on the ballot for the public to vote on during the next election.

Answer 2

What do you think Lobbyists are?

Who do you think writes most bills?