Why do you need a business entity to build business credit?
It is best to build business credit with an LLC or Corporation (S or C Corporation). Creditors, Lenders, Trade Accounts and so on prefer to see an actual business entity. Furthermore filing and using a business entity to build business credit can separate you personally from the liability of operating your business.
Unless you're required to operate as a LLP or other type of partnership (Medical Practice, Law Firm, CPA, etc.), you should create a business entity. Your personal and business credit can never be truly separated if you operate as a sole proprietorship or partnership - everything you do remains "personal".
Don't be fooled! The business credit reporting agencies will let you build business credit reports under a sole prop or partnership but these are completely worthless as everything you do under those is 100% personal which makes you personally liable for each and every business debt. Don't do it.