I just shaved my second time. I let my beard grow over the weekend and just shaved it. I strop around 30 times.. basically until it feels like its a suction.. then i did the same thing for the cotton.
It sounds like you are going from leather to linen? Is that the case? I use only leather, but I'm pretty sure you're supposed to go from linen to leather. That could have something to do with it.