I know it's supposed to be a bridge, but this is the stairs tile.
If you would like an example, this is the Victory Road in Emerald:
It does use the same stairs tile, but there are actual bridge tiles. Unfortunately it seems the only bridge tiles in the caves are horizontal bridges, while you're trying to make a vertical one.
If making tiles from scratch is the problem, fortunately there is a vertical bridge using the same style in Emerald (Route 114):
Should be able to rip the tiles from Emerald and insert them into FireRed. I don't really know much about tileset hacking so I don't know how feasible it would be to add new tiles to a tileset (or how difficult it would be to rip/insert tiles), but if it can be done I think it'd help it look a lot better.
And yeah I like the idea of having a bridge there rather than a straight path, I agree it'd look empty.