I still haven't found a weapon that I'm in love with for Yelan. I tried Stringless, but her talents are 1/1/1 so the damage bonus isn't noticeable. I'll try it again later. I tried Favonius which helps with ER, but otherwise is a bust. Sacrificial is kinda nice because then I get 3 uses of her skill in combat, but that seems like a waste because the skill (while cool) doesn't do a ton of damage on its own and is mostly there for ER. My extra Amos bow does nothing for her. Too bad "The Bell" is a claymore instead of a bow. That'd be nice for her.
Yes, the 4 star bow situation can be tricky and will determine your artifact setup (or vice-versa):
Favonius - This what I'm using. I think this ends up being the best 4 star since the ER is high enough that you can use an HP Sands and just get some ER from other artifact substats and artifact set bonuses. Also, I need to test, but if you crit with her breakthrough state barbed shot, that's another energy generation possibility
Sacrificial - I'd probably rank this 2nd if you have her at C0 like me. Lower than the Favonius ER substat, but it helps for ER being able to potentially get 2 skill charges. Sounds like you have Yelan at C1, so this bow would rank even lower for you. Even if someone doesn't have her at C1, her skill doesn't have that long of a CD anyway.
Stringless and Mouun - Burst bonus is nice, Yelan doesn't seem to benefit from the EM or ATK% secondary stats respectively. I don't have Mouun Moon to test, but depending on your team comp and artifact ER, I could see this being an interesting choice.
Fading Twilight - ER secondary is the same range as Sacrificial, but its high base ATK doesn't help Yelan much.
I'm nearly done building her, but I need a better EoSF headpiece to get the set bonus. Although she's similar to Xingqiu, there's enough differences to their play styles that keep her interesting. For me, I have to remember to mix in the breakthrough barbed shot and that her e-skill has a short CD. My only complaint is that I wish her burst last a bit longer, but generally glad I pulled for her.