I'd also second this - as a bare minimum, go down to Harris, it's very good. I particularly like the golden road, though that is further south than where Bobby's route would take you.Best of luck and enjoy Lewis (take yourself to Harris whilst you are there then ferry from Tarbet to Uig, Skye then to Inverness)
AND if not roughing it, book ahead....advised.
I've never been to Skye but have heard that it's apparently stunning. If you do go via Skye and Inverness, I'd recommend doing some of the amazing roads in Wester Ross around Shieldaig and Torridon (and the mighty Bealach na ba )
I have done the entire Outer Hebrides going south to north, and another option instead of Skye if time is not an issue would be to ride down through Harris, cross over to North Uist, go south down the Uists and get the ferry to Oban (either from Lochboisdale on South Uist or Castlebay on Barra); there's a direct train from Oban to Glasgow.