First property, now how to re-fi out of private lending

[Helene Vanderhaeghe]

I have a firm offer on my first rental property (equal parts anxious and excited)!  I waved the financing condition and I'm set to close in under three weeks.  While I thought I would be able to get financing from an alternative lender, it hasn't come through and now I'm considering private lending at 9%.  This was my worst case scenario analysis, and I'm okay with it because the house is under market value and in great shape and it's already tenanted and it gets me into the market, but it does mean that I'm making about $150 negative cash flow each month. 

My question is about re-financing at the end of the 1 year term. The issue is that I'm self-employed, so my income isn't fantastic, and I live in a city with exorbitant rents, so my DTI ratio isn't great. I AirBnB to make additional income, but the lenders won't look at that. Will it be difficult to re-finance into traditional lending?

Thanks guys!