Epcot opens at 9. Disney Springs doesn’t open til 10. The first buses don’t get to the resorts to pick up guests going to Springs til at least 9:30. The Disney Springs buses drop off in a central location, not at the resort pick up area. So you don’t just get on a bus that drops off BW or BC guests. You could be waiting a half hour or more for a bus back to an Epcot resort. Even when you get on a bus, they have a schedule & often sit waiting for 10 minutes or so before they leave. I would guess the earliest you would get back to a resort will be 10:30. And that’s optimistic. Then you’ll need at least 10 minutes to get to the IG & time to get thru security & the admission scanners.
Can I ask why you need to get to that entrance? If you’re spending the day at Epcot, it seems it would be much less hassle to get dropped off at the main entrance & just enter that way. The IG is convenient for guests staying near there, but not necessarily for anyone else. By the time you go thru all the other steps to get to IG, you could just as easily enter at the maingate at normal opening.