You will unlock the Ship feature as you progress through the initial playthrough of Borderlands Mobile.

It is located in the upper right side of the screen.

Upgrade your Ship using the Ship Parts that you have collected to meet new allies to unlock new rooms. Upgrade those rooms to get Buffs and to power up your Ship in Borderlands Mobile. 

For example:

• Upgrading the Bridge to level 2 will unlock Tiny Tina’s Tower of Terror.
  
  

• Upgrading the Scavenger Hunt to level 2 will add Parts and Fillers to the items that Vaughn will find for you.
  
  

• Upgrading Marcus Munitions to level 2 will add Rare Weapons in the store’s Free Chest.