I make hand printed/signed quilt labels. I haven't had any issues with the bleeding or the ink spreading out while I was writing on the fabric. I use the
Sakura Pigma Micron Pens -- they do come in different size tips, so you have a choice of what you like. I've tried different sizes of the tips and prefer to use the 08 size for signing my quilts as it was a better width. The 08 isn't a thick or even a medium that you would think of in a 'marker', but it wasn't as thin and light as the finer Sakura Pigma Micron Pens.
Here is a picture of the label I was putting on my grandson's quilt, to show you what the 08 size looks like.