3-4
The original 3 (not including Batman): Dick Grayson, Jason Todd, and Barbara Gordon.
Barbara Gordon joins a short time after Dick Grayson becomes Robin.
Dick Grayson has a falling out with Batman and leaves.
Jason Todd joins after Dick leaves.
Jason Todd and Barbara Gordon get killed and paralyzed, respectively.
Batman spends 10 years operating alone, occasionally accepting Barbara's help.
Luke Fox joins the "family" post BvS.
So, 4 total, but at most, 3 at a time.
And the time frame for all of this:
Disclaimer: I don't think any of them should join Batman while teenagers.
1995: The Batman begins his crusade against crime.
2000: a 20-yr old Dick Grayson joins Batman's crusade as Robin
2002-3: Barbara Gordon joins Batman's team as Batgirl.
2003-2004: Dick Grayson has a falling out with Batman, and leaves, soon after becoming Nightwing in Bludhaven.
2003-4: Jason Todd joins Batman's crusade as the second Robin.
2005: Jason Todd is killed by Joker and Barbara Gordon is paralyzed.
2015: BvS happens. Batman's spent 10 years fighting alone, and occasionally accepting help from Barbara Gordon as Oracle, but ultimately he pushes her away, not wanting to hurt anyone else by dragging them into his fight against crime.
post-BvS (2018-19): Luke Fox joins Batman's team, after Dick Grayson (as Nightwing) and Barbara Gordon (as a Star Labs-healed Batgirl) rejoin Batman.