Seshadri constants and negative curves on blowups of ruled surfaces

In this article we compute Seshadri constants of ample line bundles on the blowup of Hirzebruch surface ${\mathbb{F}}_e$ at $r⩽e+3$ very general points. Similarly, we compute Seshadri constants on the blowups of certain decomposable ruled surfaces over smooth curves of non-zero genus. We also prove some results related to bounded negativity of blowups of Hirzebruch surfaces and ruled surfaces.