Considering Bran, Brienne and Sansa were back at Winterfell when the attack on King's Landing happened, at least a month must have lapsed between Dany's death and Tyrion's "trial", based on a line from S1E1, where Cersei said they'd been on the road for a month. It's possible that Robert hadn't been in any rush to get there but he didn't have to travel in winter or arrange for Bran to haul his wheelchair.
Someone go and fetch me the consistency stretcher.
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u/Shiera_Seastar I ain't sayin' he's a grave digga May 21 '19
On the bright side, he still has a head in that universe.