Bridge Loan? Buy New Construction + Sell Existing Home after move in?

[John Wallace]

I've got a situation where I would like to buy a new construction home to be my primary residence. I am currently living in a home that I will need to sell. However, to get into the new home, I need to be able to make an offer without contingencies. So I am thinking a bridge loan might be what I need. My home should sell for more than the cost to buy the new home. We will be listing our existing home in the next week or so. But there's no way it will sell before I need to make my non-contingent offer for this new home. 

Does anyone offer a load like this? 

Current Home Value: $1,100,000 (I owe about $438,000)

Cost for new home: $950,000

As far as other assets: 

Rental 1: Value $330,000 (owe $177,000)

Rental 2: Value $196,000 (own free and clear) 

I have some stocks I could liquidate, but would rather not.