Walk, Bike, Uber, Bus
No, there is no official transportation offered by Beale Street Music Festival.
Generally this will be highly dependent on where you are staying in Memphis. If you are anywhere near Downtown I highly recommend just walking or biking to the festival. If you are staying outside of downtown you can utilize either public transportation (bus) or take an Uber. In general I recommend just taking a bus or trolley as they are far cheaper. The bus will cost you just $1.75 a ride and the trolley is even cheaper at $1 a ride. It's not uncommon for Uber to have drastically surged prices for Beale Street so try to avoid them and save some money by using public transportation.
$1 a ride to take the trolley, $1.75 for a bus ride (both costs each way)
No, there is no official parking available. There is parking available throughout downtown Memphis but expect the prices to be increased for a busy event like Beale Street.