125cc takes ages to start from cold ?
Do a "tune'up" first. Replace the plug (there is only one) and air filter. If the fuel filter is external (outside of the tank), replace it. Replace the battery. It is 4 AH battery, a $15 part. Change the oil, make sure you have the correct viscosity. Now try again.
"I'm guessing that the throttle idler nut needs adjusting for the tps sensor" A little learning is a dangerous thing. Or, in this case, an expensive thing. First look at your spark plug and read the information it will give you. Then check your battery is a) charged and b) is charging properly when the bike is running. Do the basics first then start "thinking".
Just after you turn on the ignition switch bend over to listen to the fuel pump before trying the starter. There should be a good solid sound as it pumps, if not your battery may be weak or the pump is. As stated before pull the spark plug before starting to see its condition, color on the plug's sparking end should be a dry tanish. Also check the air filter as that can restrict air flow if dirty. Next step isn't as easy- if still hard starting once you do get it to fire up ride it to my place I'll fix it up for you for a 6-pack of cold-ones (don't love working but do still remember how to). LOL!