Honestly though that's such a mood. 

Bashir's the last person Sisko has talked to in this conversation, he's turned way, not facing Sisko, so therefore misses out on the visual context clue of Sisko facing Dax, falls back not on the fact that Dax and Sisko are old friends who have shared lunch many times (whilst Julian, as far as I know/remember, hasn't shared lunch with Sisko before), but on the context clue of 'I was the last person he talked to and he didn't specify a name, so may be talking to me.'

Plus, probably, previous conversations with other people where he's ignored them whilst turned away from them (because they couldn't be talking to him, right? turning away means ending the conversation, right?) have probably ended with that person complaining about how he ignored them and acting as if it was on purpose (when really it was just because he didn’t realise it was him they were talking to.)

So when Sisko asks if someone would care to have lunch, he assumes that it could be him, therefore it would be best to make sure he doesn’t upset Sisko like he has other people by definitely responding.

Whether he even processes that Jadzia turns Sisko down afterwards I don’t know. He’s probably too busy thinking to himself ‘Good job, Julian. You did the thing neurotypicals do. You can relax now.’, without realising that that’s not the thing he should have done in that situation.

Bonus:

[ID: Benjamin Sisko and Julian Bashir having lunch together, behind them to the left is another man. To the right is a bright yellow and red wall. End ID]