Say I love a someone very much and I spend a lot of time with them. I’d like to know others ways to express knowing them. I have a few words in mind like building up a connection, a bond, intimacy, etc these words are ambiguous to me, and I end up juggling which word fits right in this kind of circumstance.
If you love someone very much, you can say that you are head over heels (in love) with that person. It doesn't have to mean that you spend a lot of time together. The idiom is just to express that you are completely in love.
To emphasize how much time you spend together, you can say that you are inseparable:
people who are inseparable are always together
If you build a connection with someone, you develop a relationship. It doesn't necessarily mean deep love. It can be friendship too.
A bond between people is a strong feeling of friendship, love, or shared beliefs and experiences that unites them. As you can see, again, it's not only about love. For example, male bonding is the forming of close friendships between men, and so if men develop a bond, they become close friends.
Intimacy between two people is a very close personal relationship between them, and the relationship is not necessarily between 2 lovers. An intimate friend is a close friend.