Plant Salvage

I am about to move out of a house that I have rented for four years. During that time, I bought several nice bushes and had the yard landscaped. I am not 100% sure what will become of them because I’m not sure they even plan to rent it out again after I go. I would really like to take the plants with me. They’re all blooming and green now but I’ve been told that they can still be transplanted. I need help getting them out of the ground and I’m hoping there is someone here with the know how to help me wit this. They’re happy plants and I want to take them with me!