Bigby's Grasping Hand
The spell Bigby's hand says:
When you cast the spell and as a bonus action on your subsequent turns, you can move the hand up to 60 feet and then cause one of the following effects with it. [...]
Grasping Hand. The hand attempts to grapple a Huge or smaller creature within 5 feet of it. You use the hand’s Strength score to resolve the grapple. If the target is Medium or smaller, you have advantage on the check. it. [..., emhasis added]
In subsequent rounds after casting, this allows you to make a grapple check as a bonus action without having made a separate attack first.
This does exactly what you ask for, but will require a rather big investment in a multiclassing to a class that can cast Bigby's hand, such as Wizard or Artificer. What are other alternatives?
If you want to effect grappling as a bonus action without you yourself attacking first, and without help by other PCs, you could take a dip in Ranger (Drakewarden) (Fitzban's Treasury of Dragons, p. 15). At third level you get to summon a Drake Companion who can help you with grappling as a bonus action (although it would be the companion who grapples, not you):
the only action it takes on its turn is the Dodge action, unless you take a bonus action on your turn to command it to take another action. That action can be one in its stat block or some other action
As the drakes action can be some other action not in its stat block, it should be able to grapple instead of dealing damage with its Attack action, which is one of the standard actions available.
The same tactic would work by taking a two-level dip in Artificer, with a Homunculus Servant, as in Raxy's answer.
For a pure fighter, I am not aware of any feat or subclass feature that would allow you to do this. The Battlemaster has a few maneuvers that allow grappling as a bonus action (Grappling Strike, and Restraining Strike), but both of them require an attack first. The Eldritch Knight's spells only go up to level 4 (so not even allowing you to cast the 5th level Bigby's hand).