Hi Patrick. You can list your current property and make an offer on the home you want to purchase and put in the contract that the purchase of the home is contingent on you selling you current home. That would tell the seller of the property you want to buy that in order for you to purchase their home, your property has to sell first. If they agree to this, you are good to go. You can even set it up that you would close concurrently, meaning that once you have an offer on your home, you would put an offer on the property you want to buy and have both deals close at the same time and you wouldn't need to get any other loan. I would recommend speaking to a professional realtor in your area about this.
There are very few companies offering briodge loans as we used to know them. If you are in a financial situation where you have lots of equity in your home or dont owe anything you will be more apt to obtain a bridge loan. Your best bet is to start with your local bank you already bank with, if no luck try a trusted mortgage company but stay away from the internet companies. Good Luck Patrick