The question of "what's the correct tire pressure for my bike" comes up a lot. For Avon tires, and other manufactures, it is strongly recommend to use the manufactures recommendations.
http://www.avonmoto.com/tech/tire-pressure-guidelines
Your best and safest bet for motorcycle performance and handling is to run the recommended pressure. You can deviate slightly depending on what you want from your tire, but the closer you stay to manufacturer's guidelines, the happier you will be. Dropping pressure provides more traction but can compromise stability and increases wear. Increasing pressure decreases traction and can compromise stability but decreases wear. Also, check your tire pressure frequently.
I've always run 40 lbs on all my Harley's. I have an Avon on my Big Dog but it's a 300 so I can't compare it to the 140 or 160 that most people use on their Harley's.
For the Big Dog (not sure of the year and model)
http://www.avonmoto.com/fitment-results
It would be nice if Avon included these tire sizes in their pressure guidelines.
Yes, I believe it's a Venom. I haven't had to replace it yet but the Big Dog dealer want's $500 mounted. I think I can find one for about $325. I usually change my own tires on the Harley and get them mounted at Cycle Gear. They don't have a machine big enough to mount a 300 and I'm not about to go old school with a crow bar and rags. My rims are black powder coated and I don't want to mess them up. I may purchase the tire myself and see if I can get the dealer to mount it for $50.