The bond is between the original caster (you) and the target.
The caster of a spell is always the same, but certain rules interactions around casting spells can be complicated by familiars, depending on the wording.
The caster of the spell is the one who cast the spell. Find Familiar makes this clear with the phrase "when you cast a spell". This does not change.
What does change from a typical casting when a familiar is involved, is the delivery of the spell. "Deliver the spell as if [the familiar] had cast the spell"
So the end result is that the PC remains the caster of the spell, but the familiar is treated as having cast the spell.
The distinction may seem subtle, but you could consider the metaphor of someone relaying a message to help make it a little more clear. For the following example scenario, treat "casting a spell" as "delivering a letter".
Wizzy the Wizard casts the spell Secret Chest through Fammy the Familiar to a wooden chest.
Situationally the same as:
Wizzy the Wizard delivers a letter through Fammy the Familiar to a wooden chest.
If we ask a question like, 'Who is the author of the letter?', there is only one answer: Wizzy. If we ask a question like 'who delivered a letter?', there are two answers: Wizzy and Fammy.
Switching back to Wizzy casting a spell, let's ask those same questions through rules interactions. If we're asking 'who is the "you" who can use an action to recall the chest from the ethereal plane after the spell has been cast?', the answer is Wizzy, the caster of the spell.
If Wizzy and Fammy were both sprinkled with Dust of Disappearance before the spell, the questions 'did Wizzy cast a spell?' and 'did Fammy cast a spell?' both have the answer "yes", so the invisibility ends on each of them.
The same logic applies to Warding Bond. In almost every instance of "you" that appears in the spell description, the antecedent is the caster of the spell, Wizzy. The only time "you" gets a little fuzzy is when talking about the delivery of the spell, such as the phrase "you touch". Since Fammy did the actual, physical touching, the spell could be rewritten in this way:
This spell wards a willing creature Fammy touches and creates a mystic connection between Wizzy and the target until the spell ends. While the target is within 60 feet of Wizzy, it gains a +1 bonus to AC and saving throws, and it has resistance to all damage. Also, each time it takes damage, Wizzy takes the same amount of damage.
The spell ends if Wizzy drops to 0 hit points or if Wizzy and the target become separated by more than 60 feet. It also ends if the spell is cast again on either of the connected creatures. Wizzy can also dismiss the spell as an action.
*-(a pair of platinum rings worth at least 50 gp each, which Wizzy and the target must wear for the duration).
With only the delivery changed, it becomes clear that the bond is between the caster, Wizzy, and the target.
As for if Wizzy can be both caster and target, let's look at the spell as a whole. Including the grammatical fragment of the material component description, there are 7 sentences in the spell's description. "You" and "the target" are listed separately in 5 of them, while they are referred to with the plural "the connected creatures" in a sixth, so it's safe to assume that whoever the target of the spell is, it's someone other than the caster, Wizzy.
On a final note, an interesting consequence of the fact that touch spells can also be cast on the self is that Fammy would be able to target their own self with the spell as long as they're wearing the other half of Wizzy's pair of rings.