Path from Sponsor Finance Credit Analyst

I currently work in the Sponsor Finance division at a smaller bank as a credit analyst intern. My position will lead directly into a full-time position within the next few months and I am looking to get some guidance about potential next steps in my career.

In my role, I get to do a lot of financial modeling and underwriting for proposed acquisitions by PE firms and search funds, which I really enjoy. The acquisitions I am underwriting are not industry-specific, firms between $1-10MM in EBITDA, and we provide senior cash-flow-based financing leveraged up to 3x. I do not have other finance experience in something like IB as of yet. I went to a college with a strong finance program, but it is not a target school for recruiting. I have completed my CFA level 1 exam and am considering pursuing further down the path to get the charter. 

I think ultimately I want to try and transition to a PE firm. However, I am unsure if the path that I am heading down will allow me to break into the buy-side. 

Am I on the right track if I want to eventually work at a PE firm or is there something I could transition to that would help get me there more directly? Would it help to get an MBA after a few years of work experience?

Let me know if more information would help!