In this note, we continue the study of Seshadri constants on blow-ups of Hirzebruch surfaces initiated in (Hanumanthu, K. et al.: Math. Nachr. 298(2), 437–455 2025). Now we consider blow-ups of ruled surfaces more generally. We propose a conjecture for classifying all the negative self-intersection curves on the blow-up of a ruled surface at very general points, analogous to the (-1)-curves conjecture in P2. Assuming this conjecture is true, we exhibit an ample line bundle with an irrational Seshadri constant at a very general point on such a surface.