To clear a sand bridge, you'll need to use Saphira's firebreath attack. Stand near the sand bridge and target it with the L button, then press and hold the A button to start charging Saphira's attack. When the charge meter is full, release the A button to unleash the firebreath. This should clear the sand bridge and open up the way forward.
Note that you may encounter enemies while trying to clear the sand bridges. Be prepared to fight them off with Saphira's claw and tail attacks, or by using your own magic spells.