SBIC Licensing Improvement Act This bill modifies the timeline and creates an appeals process for the approval or disapproval of Small Business Investment Company (SBIC) license applications. Specifically, when an application to be licensed as an SBIC is approved, the bill requires the Small Business Administration to issue such license within 10 business days. The bill also (1) authorizes an applicant whose application is denied to request a written decision for the disapproval, and (2) establishes an appeals process for such applicant. Lastly, the bill allows a state development company that meets certain qualifications to apply for an SBIC license.