The old "Team Batman" BPGD file comes closest. I've actually got a whole UF Bat Family timeline stashed in the development area, but it's not written to be what we used to call "customer-facing" when I was in tech support; it's just an author reference document.

Roughly, though, and without the dates, it goes like this:

New Gotham Generation "0"
Gryphon (alias Bruce Wayne)	Batman 0
New Gotham Generation 1
Bruce Wayne	Batman 1
Dick Grayson	Robin 1
New Gotham Generation 2
Dick Grayson	Batman 2
Barbara Gordon	Batgirl 1
Jason Todd	Robin 2
New Gotham Generation 3 a/o 6/2411		New Avalon Generation 1 a/o 6/2411
Terry McGinnis	Batman 3	Tim Drake	Robin 3 -> Red Robin 1
Stephanie Brown	Batgirl 3	Cassandra Cain	Robin 4 -> Batgirl 2

To address one of your other points, Terry's been Batman since 2398. He recruited Tim and Cassie (well, technically Tim sort of recruited himself) and was responsible for most of their training, which is why Bruce's interference with both of their careers was so roundly resented by all three.

Y'know what, hell with it, it's not the prettiest presentation, but here's a trimmed version of the timeline without the secret in-development parts:

2316
- Bruce Wayne born

2324
- Thomas and Martha Wayne murdered (not by anyone we know)

2330
- Bruce Wayne (age 14) leaves Kane's World
- Dick Grayson born

2336
- Gryphon arrives on Kane's World, assumes Wayne's identity, begins operating as Batman

2340
- Bruce Wayne (24) returns to Kane's World, switches places with Gryphon, and becomes the second Batman (later Bat Cave historians, for which read "Lena", would declare him "Batman 1" and nickname Gryphon's version "Batman 0" or "Batman Prime")
- Gryphon leaves Kane's World

2342
- Dick Grayson (age 12) becomes Robin

2342-2370
- Stuff happens

2370
- Barbara Gordon born

2371
- Jason Todd born

2375
- Bruce Wayne (59) retires
- Dick Grayson (45) becomes Batman 2

2376
- Selina Kyle (?) leaves Bruce, moves to an undisclosed location on some other planet

2377
- Helena Kyle born

2380
- Terry McGinnis born

2382
- The Joker dies

2383
- Barbara Gordon (age 13) becomes Batgirl

2384
- Jason Todd (age 13) becomes the second Robin
- Dick (53) loses an argument with a Lazarus Pit

2386
- Dick (55, but now physically more like 20) retires due to injuries
- Bruce (70) shuts down the Bat Cave
- Barbara (16) calls it quits gracefully
- Jason (15)... does not, leaving Kane's to take up a new and rather more violent career as Deadpool's sidekick, Redpool
- Bruce is not amused

2387
- James Gordon is tapped to be New Avalon's first permanent Commissioner of Police; he and Barbara relocate there when she graduates from Gotham High. Shortly after, Gordon offers Dick a job on the NAPD, which he accepts

2391
- Tim Drake born

2393
- Rose Wilson born, immediately goes on the road with Deadpool & Redpool, commencing the most screwed-up dysfunctional totally happy childhood in the history of history

2394
- Cassandra Cain born. She isn't as lucky as Rosie in the childhood department, though to an outside observer the difference may be somewhat academic

2398
- Terry McGinnis (age 18) becomes Batman 3, initially somewhat against Bruce's will and/or better judgment

2402
- Selina Kyle may or may not die (Schrödinger's Catwoman?); Helena (25) discovers her father's identity and moves to New Gotham, begins operating as the second Catwoman

2403
- Tim Drake (age 12) becomes the third Robin

2404
- Bruce acknowledges paternity of Helena and adopts her

2405
- Tim (14) meets the Cluemaster's daughter Stephanie Brown (15), deduces that girls are different (how he managed to avoid noticing this before with Lena around, no one has any idea)

2406
- Tim (15) fleesrelocates to New Avalon, founds the Titans

2408
- Terry (28) recruits Cassie Cain (14) as the new Robin; when Bruce (92) horns in and insists that she has to take the title from Tim by force, she defects to the Titans and becomes the second Batgirl instead
- Bruce disappears

2410
- Stephanie (20) becomes the third Batgirl, despite the fact that the second is still operating, 'cause that's how Terry rolls

2411
- Tim (20) revises his costume and starts going by "Red Robin"
- Tim revises his costume again so people will stop mistaking him for Dr. Mid-Nite

As you see there and in the table above it, as of mid-2411 the post of Robin is vacant (as such) and there are two Batgirls, one in each city.

--G.
-><-
Benjamin D. Hutchins, Co-Founder, Editor-in-Chief, & Forum Mod
Eyrie Productions, Unlimited http://www.eyrie-productions.com/
zgryphon at that email service Google has
Ceterum censeo Carthaginem esse delendam.