Yes, you can apply for h1b next year using your bachelor's degree. If your h1b is picked for processing, you will continue under F1 status. If the h1b is approved with change of status, your status will change to h1b from October 01, 2016. In other words, you will be in student F1 status until September 30 2016. Please let me know if it's clear or you need more information.