OK, I don’t know what I did, but it started working.
I know that it worked for you but can you remember what you did, cause I have the same problem… 
Same here. I have tried everything and the 404’s keep coming. Any help would be greatly appreciated. For now I have deactivated BP and hope that someone documents a fix.
I can’t believe that such a problem is not discussed to the point of being already solved.
I am sure that there are so many people who got wp installed in a subdirectory.
Two days ago I wrote an in-depth topic about just that. Please read it here.
It was TOTALLY ignored by the community.
I don’t care if it is the discussed here or there, as long as IT IS discussed, and not ignored.
Really, is there only 3-4 people with wp in a subdirectory and don’t want a permalink configuration such as: mywebsite.com/wordpress/activity?
C’mon…
(Oh, by the way my site does work with that setup, I just don’t want the subfolder in the permalinks, and yes, that represent a big issue for me).
I faced the same problem… and I did took the simplest measure to make it work: I shifted the WP files out of its folder… I know, not the best solution. But I’m working on a fresh site, and I could afford to…
Well, putting the files out of the subdirectory is not a solution. That is not having the problem in the first place. Not the same thing, really.
I’m currently running an active site, and having followed the instructions in https://codex.wordpress.org/Giving_WordPress_Its_Own_Directory I’ve got all my files in a mysite/wordpress file with everything in the wordpress folder but the index.php and .htaccess files in the home directory. that’s given the whole of my site a mysite address rather than a mysite/wordpress address.
This sites been up a while and works well, but I’m having trouble getting BuddyPress to work on it. Whatever I try, I seem to end up with half the site still on mysite (whilst everything in mysite/wordpress is coming up unobtainable); or half the site on mysite/wordpress (whilst everything in mysite is unobtainable).
There’s quite a bit of activity on the site, so I don’t want to start from scratch, but I would like to get BuddyPress on it. Has anyone worked out how to do this yet?
I tried the solution at https://buddypress.org/forums/topic/permalinks-setup-with-wp-intalled-in-subdirectory-and-indexphp-in-root?replies=23#post-45920 (which is marked “Resolved”) but it didn’t work for me.
