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.