It won't work, because the character believes it's already real
The text of the spell states, (emphasis added)
While a target is affected by the spell, the target treats the phantasm as if it were real. The target rationalizes any illogical outcomes from interacting with the phantasm.
This means that the illusionist believes that the illusion that he/she is seeing is already real, and is thus not a valid target for illusory reality. This doesn't really make sense, but the spell is very explicit that any illogical outcomes are rationalized away. Perhaps they think that casting and concentrating on the spell is necessary to reveal the bridge, or some magic mishap made the bridge real. Still, the bridge is still not real, and the wizard's party members would fall through it (in fact, they wouldn't even know that it's there).
Moreover, if the wizard does somehow realize that the illusion is just an illusion, the spell ends and the illusion disappears:
If the check succeeds, the target realizes that the phantasm is an illusion, and the spell ends.
Your scenario depends on metagaming
Your scenario's logic requires that the wizard hold contradictory beliefs: that the illusion is real, and that it's not. The only way to resolve the contradiction, and thus use this "exploit", is to use out of character knowledge that the character itself cannot have. Accusations of metagaming often get quite hairy, but I think that this is one of a few clear-cut situations.