I feel Miller’s post directly above yours applies here.
ETA Spice_weasel’s post appeared just as I hit post. Bah!
“Jet Boy Jet Girl” — the narrator doesn’t sound bi but the object of his affections does
“Drop the Pilot” - the narrator’s trying to seduce a woman out of her straight relationship.
Also by Armatrading: “Me Myself I” — the narrator wants a boyfriend “and a girl for laughs” (could be a bestie, I suppo-ose …)
Only in 3’s by The Breeders:
“My Girl Bill” by Jim Stafford. The song flirts hard with gay themes and innuendo, though by the final verse it’s all put safely back in the closet and they’re two dudes in love with the same woman. Pretty edgy stuff for 1974 AM radio fare. Jim Stafford - My Girl Bill - YouTube
These are just ripped off blues lyrics. This is all about being the guy cuckolding the husband…not bi IMHO
Could be. Mr. Morrison would probably be horrified at the myriad ways white suburban teenagers have misinterpreted his songs over the years. 
Does Dodie, a popular youtuber with almost 2 million subscribers, count as a popular artist for this thread?
I’m confused. Your thread title says you are looking for “implicit” songs but your text implies you only want explicit songs.
Anyway, an implicit example is Cindy Lauper’s “When You Were Mine” which (to my ear at least) manages to create an audio confusion between the words “guy” and “girl.” It sure sounds like a girlfriend who is upset because her (male? I guess I just assumed that) lover is seeing someone else, of male or female gender, and he/they doesn’t have “the decency to change the sheets.”
I’ve always thought that song was admirably gender-ambiguous. But I may be wrong.
Well, that song was written by Prince, so the gender ambiguity is baked in. Just like in his song If I Was Your Girlfriend.
What about Ode to Billie Joe?
It was already mentioned that trans != bi, but a better and IMHO perfect example is the Kinks’ “See My Friends”:
Right. “Back Door Man” was a Willie Dixon number about a guy who was sleeping around with other men’s wives. He slips out the back door when the husband comes in the front door.
Although there’s definitely some double entendre going on with “back door”, I never actually got any kind of gay or bi vibe from it.
Esperanza Spalding’s version of I Can’t Help It.
It’s a cover of a song originally recorded by Michael Jackson (songwriting credit is Stevie Wonder and Susaye Greene).
The lyrics of the song are perhaps implicitly bisexual, at least as interpreted by Spalding, but the video makes it explicitly clear.
So I’m not sure this meets the OP’s criteria. I think it might.
Somehow I got the wrong link in the post above. Here’s the right one -
And then there’s this.
Loving the responses, and adding to my playlist.
Willie Dixon was terrific. Many years ago we adopted a couple of cats and named them Jimmy Morrison and Willie Dixon. I always said “Back Door Man” was their song.
By “double entendre” were you referring to “back door” being a euphemism for anal sex? I always assumed that was part of what the little girls understand.
It probably isn’t quite right, because it’s a novelty song that is meant to be funny, but the 2 Nice Girls’ song “I Spent My Last $10 on Birth Control and Beer,” is a woman lamenting that she ruined her life by taking up with a man after being with only women previously.
Great song, and I’ve seen it live a couple of times.
One that is difficult to suss is Raspberry Swirl, but many Tori Amos songs are a challenge to interpret.