The equity in the home you are selling
A bridge loan is sized against the equity in your current home after the mortgage already on it. The less equity there is, the less a bridge loan can do and the more it costs relative to what it does.
A home that will sell, and a plan for selling it
The loan is repaid by the sale, so the sale is the underwriting. A home priced to the market and ready to list is a different file from one that may sit. Expect questions about how it is priced, when it goes on the market, and what the plan is if the first buyer falls through.
Carrying both payments until it closes
Until the sale closes you are responsible for the payment on the home you are leaving, the payment on the home you are buying, and the bridge loan itself, however it is structured.
Which kind of bridge loan it is
A bridge loan on the home you live in, to buy the next home you will live in, is a consumer loan: when it is a closed-end loan from a lender federal rules count as a creditor, it comes with a Loan Estimate and a Closing Disclosure like a standard mortgage. A bridge loan whose money buys or carries a rental or an investment property is a business-purpose loan, outside those consumer rules, with none of the federal disclosures a home loan carries. What decides it is what the money is for, not which property secures it: a loan to buy the home you will live in is a consumer loan whatever it is secured by. Which kind you need changes which lenders can write it.
Where it is not the answer
If the equity is thin or the home may not sell soon, a bridge loan adds cost to a problem it cannot fix. A HELOC opened before you list, a contingent offer written carefully, or selling first and renting back from the buyer may serve you better.