It's hard to find, no real signage or anything, but there's a link to the harborwalk by Porzio Park, from there sidewalks take you to Terminal A (from there you can keep going on the sidewalk or get on a shuttle bus to the right terminal). You can even stop off at the very well hidden 9/11 Memorial on your way.

There's also a path that goes from the Blue Line Airport stop to Terminal E, so if you lived on that side of Eastie you can walk over the tracks at airport station and then walk in that way.

The whole place isn't particularly well designed for pedestrians but I was surprised the first time I did it at the completeness of the sidewalks and pedestrian signals at traffic lights

There are roads with sidewalks around the airport, one of which leads to the bus terminal. Not sure exactly the route but it’s possible.