Trim the flower from the novelty device. Cut through the tubing near the base of the flower using scissors. If the tubing is tough, try wire snips to get through it.
Find tubing of the right size to fit over the trimmed end. Take the squeeze bulb with you to go shopping in a hardware store and test the tubing in-store to find a width that fits snugly over the tube on the bulb. Purchase more tubing than you think you'll need.
Attach tubing to the extend the tubing on the bulb. Insert the end of the bulb tube into the purchased tubing. Make sure there's enough overlap between both pieces to ensure that the fit is tight and won't easily tug loose.
Thread the tubing through your costume to determine the appropriate length for the excess. Figure out how the tubing will wrap around your body, where it should end and where the squeeze bulb will be hidden, like in a pocket.
Test-fire the squirting device using water. Fill the device by submerging the end of the tube in a container of water, then squeezing as much air as you can out of the bulb. Release, and the bulb, as well as some of the tube, will fill with water. Practice squeezing to see what kind of pressure produces the spurt you want.
Mix a blood solution. Add enough water to your stage blood to make it almost as thin as water, if it's not already there. If this makes the color too light, add a drop of red food coloring.
Fill the bulb with blood. Wipe off the end of the tubing to avoid getting blood on your costume before the appropriate time.