The more positive time you spend with your dog the closer your relationship will be. Positive training is a great way to have a bonding time together. It's not stressful and can be enjoyed by all. It also builds the communication between you and your canine.
Another good way to bond with your dog, especially a newly acquired dog, is to attach the dog to a leash and hook it on your belt. It will ensure that the dog remains with you. It is also a good way to keep a watch on the dog when you are trying to potty train. You will avoid accidents by not allowing the dog out of your sight. It can help in curtailing any problem behaviors before they start. Your dog won't be able to chew things up or knock over the garbage because they will be attached to you.
Take your dog for a car ride. Many dogs enjoy traveling in a car because it oftens gives them something else to do.
When we brought our dog Dutch home she wasn't used to living in a house. She was a four month old puppy that had lived on an Amish farm. She was terrified of being around us and would often find a place to cower. It took her about two weeks to adjust and bond with me. I spent time just holding her next to me on the couch and petting her. I knew at first she wasn't really comfortable with that but slowly she learned to relax.
She ended up being my all time favorite dog. We had a really closely bond that I have never had with any of my other dogs. She was probably a once in a lifetime dog and my husband accused me of loving the dog more than him. Needless to say we were almost inseparable. I would take her everywhere with me. She even traveled with us on long trips. She was also what I call a naturally obedient dog because she would come when you called her without any formal training.
Unfortunately she only lived 1 1/2 years with us. She ended up getting into some sort of poison that we didn't realize until it was too late and her liver was badly damaged. It still brings tears to my eyes when I think of her.