To increase your bond with a companion in Scarlet nexus, you will need to first have them in your party for a certain amount of time. Eventually, as you and your companions fight alongside each other, your bond will gradually increase.
However, there are a few more to increase your bound quicker than waiting for the bar to increase. The first is to give your companions a gift. You can get these gifts either by exploring the world and looting the many white crystals you will come across. Along with exploring, you can also purchase gifts from the shop next to Satori the Archivist.
Once you got one of these gifts, you can then give it to one of your teammates by finding them in the hideout area once it becomes unlocked after phase 2. When you give a gift to one of these teammates, they will either like, love, or adore it, and each feeling will raise your bond with them by a certain amount.
Adore will also give the highest increase, so it is ideal to get that reaction. However, you will need to experiment with gifts, as each NPC has things they like and don’t like.
Beyond gifts, you can also increase bonds by completing bond episodes. These are events that will happen at various points of the game, and each companion has one the player can complete. Upon completion, you will get a huge increase to your party member’s bond level. But before you can start these episodes, you will need the hideout unlocked.
At this point in the game, you will then be able to start bond episodes when your companions have icons over their heads indicating they have an episode available to complete. That said, after you increase a bond, you will be able to unlock more abilities you can use with your companions along with improving ones you already unlocked.
For more on Scarlet Nexus, check out Where to find Buddy Rummy in Scarlet Nexus and Where to find Auger Sabbat in Scarlet Nexus?