You can do this with the bleed settings and artboard placement fairly easily. However, you must do it manually. Illustrator doesn't think in terms of "pages" and "spreads".
Start with 1 artboard and a set of rectangles that represent your trim size pages. Here I have 1 artboard then 6-8.5x11" rectangles. I've arranged the rectangles to represent page spreads.
The reason for using rectangles to set this is up is because rectangles will snap to each other and you can align them using alignment tools. None of that is possible with actual artboards. So, set up the rectangles and then select them all.
Object > Artboards > Convert to Artboards.
Then, with the Artboard Tool, click that first artboard and delete it. You're left with 6 artboard set up like pseudo "pages".
To add the bleed, choose
File > Document Setup and enter the bleed amount you wish:
That will add guides to each artboard for the bleed (red line):
A closer view shows how the bleeds will overlap in spreads as they are supposed to:
Be aware that when you output, there won't be any option to output spreads the way InDesign will. If you need spreads output, you'll need to create additional artboards the size of spreads (which can overlap the individual "page" artboards), then output those "spread" artboards rather than the individual artboards.
There may be a script out there somewhere to automate all this. It's really just the same set up every time with varying "page" counts. But as far as I'm aware, nothing in the "vanilla" install of Illustrator will do this automatically.
Quite honestly, in terms of output, it's often easier to go ahead and build the individual pages in Illustrator with their bleeds, then
Place them into InDesign as single pages just for the page configuration and output options. If you have to move or rearrange pages, it'll be very troublesome in Illustrator. But if everything in Illustrator is merely a single page placed into InDesign, you can rearrange InDesign pages, output single pages or spreads with a 2 second change. Just in terms of sheer output logistics, placing pages in InDesign makes things much easier.
I have had this same issue and can only do it the manual way.
Illustrator has Artboards, not pages - right? Each Artboard has to be the size of the bleeded spread (for example 17.25" wide x 11.25" tall). I like to automatically add crop marks of the 8.5x11 sheet by drawing 8.5x11 boxes and then select menu EFFECTS > CROP MARK.
Another idea is to export your final Illustrator Artboards to InDesign spreads. And then let InDesign take it from there (Save as PDF with cropmarks).
Is this too manual or were you hoping for a one-click answer?