Long, but the exact number is not important.
Your streak of losses doesn't even earn honorable (dishonorable?) mention. I have lost the first 20 hands after sitting down; no pushes, no insurance, no surrender, no cocktail waitress. The good news is that it was negative all the way, so nothing more than a minimum bet.
If you put in the hours, you will see similar things occur. It's all part of the game. Try to take it in stride. Better for your long term health.