That was just one instance but he has also been shown to give Luffy advice and tell him what is best during dire situations.
Also, during Punk Hazard when he said that they shouldn't fool around anymore and start getting serious since this is the new world. Zoro has shown at times to tell Luffy to pull his head together, and him being worried that he might do something stupid so he questions it.
Not saying that the bounty matters, but I hardly see Vice Captains with low bounties and Zoro has always been close to Luffy when it comes to bounties so that should be a small sign.
No one in the crew specifically assigned someone to be Vice-Captain.
Zoro seems to be the 2nd strongest so we tend to correlate that with vice-captain status, but that ain't always right. Also, a lot of people in OP have this thing for Zoro. Always making comments about "why he isn't the captain?" and "how is he so strong?"
Bartolommeo refers to him as the Vice-Captain in his point of view. Until Oda confirms with what Bartolomeo says to be true, we'll keep making our own assumptions. But seeing as how Oda has made many people assume Zoro as VC, he must be feeling something about Zoro being VC.