20.4 mile ride:  Begin from the "Shoppes on the Parkway" shopping center located on 321/221 on the NE side of Blowing Rock.  Turn left out of the parking lot onto 321/221 north and go .7 miles to the Blue Ridge Parkway on-ramp.  At the top of the ramp take the Parkway south (turn right).

Exit the Parkway at mile marker 305 at the 'US 221 Linville' exit. 
Turn south onto 221 (right).  The Grandfather entrance will be on your right after one mile.  Enter the park and head to the top. 

Note: an entrance fee of $14 per adult is required for vehicular traffic.  This fee may be waived since you are on a bike and will not be enjoying the park like others but there is no guarantee - be prepared to pay.