Integral of product of exponential and modified Bessel function

Question

I need to evaluate or upper bound the below integral for arbitrary real positive values of $(a,b,r)$: $$\int_{\phi=0}^{2\pi}\frac{\exp\left(-a\cos(\phi)\right)\cdot\mathrm{I}_1\left(2r\sqrt{b+a\cos(\phi)}\right) }{\sqrt{b+a\cos(\phi)}}\mathrm{d}\phi$$ Thanks.