This is not the asnwer to your question though. I just mentioned it because it really is the easiest way by far, very, VERY far. Even without friends you could manage to get people for it using LFG, TA sessions or even the public lobby browser the game offers.
Still, this does not answer your question
(Disclaimer: I'm not some horde master)
I'm thinking for solo play it depends what map you're trying to do.
Example: on blood drive I think Jingle Juvies would be pretty easy with the grenade class (I forgot the name). On blood drive in particular you can block off the doorway with a few barriers and plant shocks/incendiarys/frags. That could work I think.
For other maps, such as Sandbar, that probably would not work due to it being very open. This is where it gets difficult with one person. I feel like the infiltrator is pretty good for taking out the smaller enemies, giving you space to keep moving around the map when you get pressured.
Another idea would be the class with the Silverback (also forgot the name of the class). Upgrading the ultimate cooldown perk to max prior to starting the wave. Using the salvo cooldown card and explosive damage silverback heal card. You can keep using the silverback for quite a while before it running out, cleaning up most enemies (best in jingle juvies). After getting out, doing damage will speed up the cooldown of your next ultimate use massively. Using your dropshot on one of the scions which will spawn on the bosswave will get half your ultimate back.
This was me thinking out loud basically. This could've been a lot more detailed but I hope it helps a little or gets you started on a different method. It's been a long time since I played horde so I don't know everything anymore unfortunately
