I moved 15 minutes from my old house. I had styrofoam coolers to move everything. I used the same boxes to plant them in for the first two growing seasons. For two reasons. It gave me time to see where I wanted everything planted and I could give them good soil until I amend the garden soil sufficiently.
Since you have had your bulbs so long and you are taking the time to dig them up (I know that is a big undertaking) If they have been in the same planting area for years they usually have pulled themselves down to the death of HE Double hockey.
Good Luck with your move and may your future garden endeavors at your new home be blessed and fruitful.