Bashir and O'Brien did not just have what the official startrek.com website refers to as a "homosocial" relationship.
I think the writers did kind of start off with a bromance, and then the slashfic writers fans got a hold of it, and then this game of "chicken" ensued where the innuendo got more and more explicit.
There are many, many such moments: one comes from Field of Fire
O'BRIEN: The kid's a born helmsman.
BASHIR: And so say all of us.
ALL: Hear, hear.
ILARIO: Thanks. I'm just glad to be here.
O'BRIEN: It's the best posting in the galaxy.
BASHIR: If there's anything you want, anything at all, just ask.
ILARIO: Well, there is one thing.
O'BRIEN: Name it.
ILARIO: Next time you two go to the holosuite, I'd like to come along.
O'BRIEN: Sorry.
BASHIR: Can't be done.
O'BRIEN: No, it's out of the question.
BASHIR: It's impossible.
KIRA: Don't take it personally. They're very serious about their leisure activities.
BASHIR: It's a good way to relieve stress.
O'BRIEN: Yeah, I highly recommend it.
BASHIR: Just not with us.
O'BRIEN: No. You know, when you have a holosuite visit, it's sort of a personal experience.
BASHIR: He's very particular about anybody seeing him in his coonskin cap. You understand.
ILARIO: I suppose.
QUARK: Gentlemen, your holosuite is ready.
BASHIR: Terrific. Now if there's anything else you need?
O'BRIEN: Just let us know.
(O'Brien and Bashir go up the stairs)
ILARIO: Have you ever gone to the holosuite with them?
KIRA: Me? Never.
EZRI: I know when I'm not wanted.
The moment is even odder because we know from episodes like A Simple Investigation and Badda Bing Badda Bang that O'Brien and Bashir did go to the holosuites with others, including Jadzia Dax, for fun -- but when they went alone, together, they did not want anyone else to be there.
...But to me the real finishing piece is from Extreme Measures:
O'BRIEN: I should've left a note for Keiko to let her what we were planning.
BASHIR: Why worry her?
O'BRIEN: No, I want her and the kids to understand why I had to do this.
BASHIR: She'll understand. She'll know you did it for me.
O'BRIEN: That's what'll upset her the most. She always said I liked you more than I liked her.
BASHIR: That's ridiculous.
O'BRIEN: Right. Yeah.
BASHIR: Well maybe you do, a bit more.
O'BRIEN: What? Are you crazy? She's my wife. I love her.
BASHIR: Of course you love her. She's your wife.
O'BRIEN: Yeah.
BASHIR: I'm just saying maybe you like me a bit more, that's all.
O'BRIEN: I do not.
BASHIR: You spend more time with me.
O'BRIEN: We work together.
BASHIR: We have more in common.
O'BRIEN: Julian, you are starting to annoy me.
BASHIR: Darts, racquetball, Vic's lounge, the Alamo. Need I go on?
O'BRIEN: I love my wife.
BASHIR: And I love Ezri. Passionately.
O'BRIEN: You do?
BASHIR: Yes.
O'BRIEN: Have you told her?
BASHIR: Not yet. But I will.
O'BRIEN: Oh, yeah? When?
BASHIR: When I'm ready. It's just that I like you a bit more. See? There, I've admitted it.
O'BRIEN: Yeah, well, I love my wife.
The dialogue doesn't even really do it justice, I don't see how you can watch that scene and conclude something other than that they had a romantic relationship.