First, post-Civil War, I decided to alternate New Avengers and Mighty Avengers with it going New Avengers #27, Mighty Avengers #1, New Avengers #28, Mighty Avengers #2, and so on until you get to Mighty Avengers #11, which is followed by New Avengers annual #2. This leads right into Secret Invasion and the order I've decided upon:
- New Avengers #38-39: "Infiltration" issues.
- New Avengers: Illuminati #1-5: This series needs to go somewhere and here seems best since issue one sets up Secret Invasion and issue five is a lead-in to Secret Invasion.
- Secret Invasion #1. The story begins with various reveals of characters as Skrulls. Since many issues deal with how people were replaced, having those issues before the actual reveals wouldn't make much sense.
- New Avengers #44. Skrulls use fake Illuminati to attempt to harness Reed Richards's intellect. Seems like the 'earliest' plot and builds directly on the Illuminati series.
- Mighty Avengers #16. Elektra explanation.
- Mighty Avengers #15, 17. Hank Pym issues.
- New Avengers #46. The Hood and his group discover the Skrulls prior to the invasion.
- Secret Invasion #2. The fight in the Savage Land leads into other tie-in issues.
- Mighty Avengers #14. Sentry issue that builds on what happens in the Savage Land.
- New Avengers #41, 43. Spider-Man meets up with Ka-Zar and Sheena during Savage Land fight. Most revelations from the past, including the Skrull Captain America.
- Secret Invasion: Who Do You Trust?. Not a Bendis issue, but I have it, so I'm mentioning it. At least one story builds on the Savage Land fight.
- Secret Invasion #3. The Skrull Queen is revealed to be Spider-Woman.
- New Avengers #40, 42, 45. The Skrull Queen's three-issue storyarc as she is found by her people and takes over for Spider-Woman.
- Secret Invasion #4-5. Main plot.
- Mighty Avengers #19. Captain Marvel/Noh-Varr issue that builds on events in Secret Invasion #5 and leads into/crosses over with Secret Invasion #6.
- Secret Invasion #6-8. The story concludes.
- New Avengers #47. Luke Cage and Jessica Jones story that ties into fall-out from Secret Invasion #8.
- Mighty Avengers #20. An epilogue to the whole thing.
What you may be wondering is "Where's Mighty Avengers #12, 13, and 18?" and the answer is simple: I pulled them out and stuck them in front of Secret Warriors #1. That's a personal choice, but if you want to include those issues in the above, I'd slot them in between Secret Invasion #3 and 4, right after Fury and company shows up in that "shocking" manner.
So, there is your Brian Michael Bendis Secret Invasion issues reading order. I'm sure many will disagree including Bendis himself who I imagine would argue for just reading them in the order they were published, but I prefer this way.
UPDATE 06/29/13: In doing a reread of Bendis's Avengers work, I decided that my original placement of the Skrull Queen/Spider-Woman issues of New Avengers after Secret Invasion #1 was incorrect. I have moved them to following Secret Invasion #3 where the reveal that Spider-Woman is the Skrull Queen happens. While the Skrull Queen is shown in some of the other New Avengers and Mighty Avengers spotlight issues that I place earlier in the reading order, she's always shown out of costume and come off as a generic human woman, not Spider-Woman specifically.