What do I do with dead/dying spring bulbs?

Despite being in my 50s, I have only come to gardening this last two years. I say "gardening" - I have a raised "thing" - a big rectangular wooden box on legs - that my husband bought for me last year when I expressed an interest in growing vegetables. That was literally my first ever foray into growing anything. Oh apart from some mint, which I managed to kill off

We had tomatoes, rosemary, lettuce, carrots, peas, onions and something else that I now forget! Oh and strawberries in a hanging planter. Quite successful.

I kind of caught the bug, so this year I am repeating the experiment with things in the trug (I call it a trug - I have no clue what the correct name is for it!) and have planted seeds to grow more vegetables, and I have also bought a plastic greenhouse type thing from Cuticave (a bargain at a car boot sale) and I have got a tomato growbag with three tomato plants in it, and some courgette plants in there.

I am definitely not into digging up the garden, so I have gone container-crazy!! I have about six different containers that I planted with bulbs. We had some lovely daffodils, crocuses, hyacinths and something I don't recognise and don't remember planting, but which were very pretty

All the bulbs/flowers are now at an end, apart from four tulips which are still flowering nicely.

But what do I do with the other dead/dying bulbs? Do I have to throw them away and plant new ones in the autumn ready for next spring? Or just leave them in situ? I'd quite like to put some different things in the container to give a bit of colour in the summer/autumn, but I truly have no idea what to do with the bulbs that are in there now.