Consider the weight of the cyclist of weight mg moving around a curve of radius r. Generally the cyclist leans inward making an angle Ɵ.

The forces acting in this scenario are

1. Weight mg of the cycle and cyclist acting vertically downward
2. Reaction R of the ground on the cyclist. It acts along the line making an angle Ɵ with the vertical, the components of which can be divided into cos Ɵ and sin Ɵ
3. Resolving the horizontal and vertical components we get

mg = r cos Ɵ

mv² / r = r sin Ɵ

Solving the equations we get Ɵ = tan^-1 (v²/rg)

The angle through which the cyclist will have to bend will be greater if (a) velocity is large and (b) radius of the curve is small

Hence, bending inward for cyclist is much needed.