There could be several reasons why your YZ 250 2-stroke motorcycle is starting only when it's bumped and then kick starts afterward. Here are a few possibilities to consider:
Weak battery: If your battery is weak or not holding a charge, it may not have enough power to crank the engine and start the bike. When you bump-start the motorcycle, it gains enough momentum to turn the engine over, which in turn generates the power needed to charge the battery. Afterward, the kick starter may be able to start the engine because the battery has gained some charge. Consider checking the battery's voltage and condition.
Faulty starter motor: The starter motor may be experiencing issues, such as a worn-out or damaged starter gear, a faulty solenoid, or a weak starter motor itself. Bump-starting the bike bypasses the starter motor, allowing the engine to turn over, but using the kick starter later on utilizes a different mechanism to start the engine.
Ignition system issues: Problems within the ignition system, such as a faulty spark plug, ignition coil, or CDI unit, can cause difficulties in starting the motorcycle. Bump-starting can sometimes help overcome these issues temporarily, allowing the engine to fire up. However, the kick starter may struggle if the ignition system problem persists.
Fuel delivery problems: Insufficient fuel flow, clogged carburetor jets, or a malfunctioning fuel pump can hinder proper fuel delivery to the engine, making it harder to start. Bump-starting might provide enough momentum to draw fuel into the engine, but the kick starter alone may not generate sufficient suction to start the engine without external assistance.
Engine compression issues: Reduced compression due to worn piston rings, cylinder damage, or improper engine assembly can make it difficult to start the bike. The additional force from bump-starting can help overcome the compression issue momentarily, allowing the engine to run. However, kick-starting alone may not generate enough compression to start the engine without assistance.
It's important to have a qualified mechanic diagnose and address the specific issue with your YZ 250. They can inspect the motorcycle, perform tests, and provide a more accurate diagnosis based on the symptoms you've described.