What do you want to do? Assuming the bulbs are healthy you could do either. Though it's a bit early in the year to worry about...
If you favour containers you could fill them now with a mix of compost, grit & leaf mould so things were nicely set up for late September planting

If you have fed the old bulbs after they had flowered to re-build the energy then perhaps re-plant some of them in early autumn. Personally, with the exception of the Daffodils, I would plant them in the ground as they, especially the Hyacinths, will not come up to expectations when they flower next year.

I am just finishing repotting my spring bulbs and would recommend they be out of their pots for as short a time as possible.

I was doing that yesterday with daffs and hyacinths. daffs were checked for narcissus fly grubs, none so far. the hyacinths produce a smaller more delicate flower spike and I find that so much nicer than the big blousy blooms. Some go in the garden others [the bigger bulbs] back in pots. Only a few had any new roots

Thank you all for your advice, very helpful.