•  it is not a shuttle connecting the two locations - it's at least two public bus lines it refers to
  
• it is public bus line 50 operated by Valley Metro passing by Brownsville Airport leading to Port Isabel and vice versa
  
• You can download the route and schedule here
• Than you change in Port Isabel to the "red" line operated by Island Metro  leading to South Padre Island, hop out along the rout and head to your hotel and vice versa
• You can download the route and schedule here ( its a big detailed file, please patience)

Now you have all the facts and time-tables at hand and it should be easier to decide how you want to reach the beach,

the sand on the beach is still the same no matter how you reach it, it might just tickle different if soar8-)

Michael with spi-shuttle.com