After recently putting a 13-56 set on my Ibanez hollowbody in standard tuning, I was told I would probably need to adjust the truss rod a bit as well as the intonation, which I expected. After waiting on it a day, I can see that the action is higher on the higher frets than it is closer to the nut, however the neck doesn't appear to need a truss adjustment. Should I adjust the action on the bridge for more consistent height? I don't think the nut would be the problem since I moved to heavier strings. Any help is appreciated.
why are you in standard tuning on a 13-56 set.
Jumping on dat gear sig train.
PRS Hollowbody II / BKP Warpigs
Strandberg OS6T / BKP Aftermath
Strandberg OS7 / Lace Poopsticks
Skervesen Raptor 7FF / BKP Warpigs
Skervesen Raptor 6 NTB / BKP Juggernauts
Hapas Sludge 7 FF / Hapas Leviathan
Anderson Baritom / Motorcity Nuke BKP Sinner Anderson H2+
Warmoth Baritone / BKP Piledriver
Ibanez Rg2120x / BKP Nailbomb

Blackstar ID:Core Beam
It's not uncommon for jazz guitarists to use heavier strings. A great guitarist I studied with used 14s himself. I'm not sure I'd ever want to go that far, but I think the 13s sound wonderful and they don't budge. Good for real heavy strumming too. I've always preferred heavier strings.
Is it a true hollowbody with a floating bridge and a trapeze tailpiece? If it is, I find it a bit unexpected that the action has got higher with heavier strings, and it makes me wonder if there is a lot of strain on the neck joint or upper bout. But yes, if the neck relief is OK, then lower the bridge - you can often get by with a lower action with heavier string because there is less string excursion.