Bike misfires on one plug for first 20 miles, then runs fine?

SOURCE: 1995 Suzuki DR650 still running rough

sounds to me like your jets are running rough, wich makes you loose power and make the bike run like sh*t, so simple re-jet it (65-75 dollars) and it will be running like a charm again

SOURCE: Bike stalls from time to time

the fuel filter is inside the tank, be sure your thorughly cleaned the tank of expired gasoline, clean the jettings again on the carb, those are so tiny particles you think cleaned already. Change the hoses too, they have a life span and the particles from the old hoses goes to the jettings. Your prob is definitely fuel based prob

SOURCE: 1986 Suzuki GS 450 won't start

Take the carburetors apart and either rebuild them or clean them thoroughly.

SOURCE: Suzuki TS125R (1994 model), not TS185: Trouble starting

It sounds like the air/fuel mixture setting is not correct i dont know the setting for a ts125 but you can always go to ebay.com and buy a service manual for that bike and it will tell you all the correct settings for the carb.

SOURCE: 1995 Suzuki DR650 running rough

Ignition timing is preset and only very badly worn camchain or valve-train issue would have an effect.

You may have a problem with the floatbowl height.
It is an incremental fix, in that you set it and see how it responds.

The fuel availability is governed by the height of the float levels. This can be adjusted by bending the small brass tab on the float spindle. Try adding more fuel first, or bend tab upwards very slightly. you don't have to remove the carby every time, just loosen the front and back manifold clamps and rotate carby so you can acces float chamber screws. The float pin can be pulled out and tab reset. Don't forget to turn fuel off and have a spill tray ready when undoing floatbowl drainplug each time.
Site below has exploded view of the carby with part names, links to all sections of the bike.
Clean all the jets with a carburetor solvent and check fuel line for perishing. Are inlet manifolds in good condition and not have a chalky feel on the insides, they should be shiny and feel slippery for efficient results.

Goodluck, cheers!

http://www.cmsnl.com/suzuki-dr650-1995-rses_model13242/partslist/FIG-11.html