There are a few potential concerns with this plan. Some of them work out in your favor, others do not.
Bonus action between attacks
You can take bonus actions between attacks, per the answer to this question.
Using both hunter's mark and zephyr strike
You can apply one spell to the first attack, and the second spell to the next attack. Of course, hunter's mark will end, but you'll still have access to the additional damage and advantage from zephyr strike.
Casting hunter's mark without initiating combat
This is the tricky part. "Initiating combat" isn't quite the right phrase here; there's no action you can take that will definitively do so. Whether combat has started is the DM's decision. However, it is possible that they will decide that combat has begun once you cast the spell. This is because the spell has verbal components, and casting it may make some noise.
If you are relying on being hidden to keep you out of combat, casting this spell may give away your position, potentially costing you the element of surprise. However, at a range of 90 ft, it's entirely possible that you can do so without attracting attention.
Benefiting from Dread Ambusher
Exactly when you benefit from Dread Ambusher is a bit tricky in these situations, but you should gain its additional attack at some point. If your targets have particularly good hearing (perhaps they've tamed a creature with the Keen Hearing trait,) your targets might be the ones initiating combat. In this case, you'll still have all the benefits you describe, it's just that your opponents might have already begun moving against you before you use them.
If you remain hidden after casting your first spell, all should go as you describe.