If the symbol r represents the radius, then dr would represent a small increment in radius. For an element of arc length, we could use ds.
If I do that, then your expression for the current in the arc length ds is dI = ds/2πrL * I. I interpret this as dI = ds/(2πrL) * I. That is, I assume that you meant the denominator to be 2πrL. If you check your dimensions (or units) you can see that this expression can't be correct. In order for the right hand side to represent a current, the quantity ds/(2πrL) would need to be dimensionless. But you can see that it has the dimensions of 1/length. However, your expression is fairly close to the correct expression.
The way to think about getting the correct expression for dI is to realize that the entire circumference of the cylinder contains the current I. The length L of the cylinder is not important here. So the current dI is the current contained in the fraction of a circumference subtended by ds.
The magnetic field that acts on the current dI is not the magnetic field, Bo, at the outside surface of the cylinder. This is kind of tricky. In reality, the current on the surface of the cylinder does not have zero thickness. So, imagine that the current occupies a very thin layer of thickness δr as shown in blue in the attached figure. The B field is not really discontinuous at the surface of the cylinder. It is zero at the inside surface of the layer of current and Bo at the outside surface of the layer. The B field changes continuously from 0 to Bo as you go through the layer of thickness δr. Different parts of the current in the layer experience different magnetic field strengths. If you imagine that the B field increases linearly from 0 to Bo, what is the average value of B in the layer of current?
