Hi, this is a clue:
The Servo will just jitter while the Arduino connects and disconnects in the second case
The Arduino resetting usually means the servo is drawing too much current. You really need a separate power supply for the Servo, or external power to the Arduino.
Maybe your breadboard has just enough added resistance that the servos does not reset the Arduino.
BUT: You never say where the power is coming from... IF USB then it's unlikely it will work. Try connecting an external power supply of 9 to 12 volts to the Arduino external power connection.
Other solutions for more Servo power, and more servos:
An UNO compatible with higher-power voltage regulator, like the YourDuino RoboRED with 2 Amps available.
OR a "Sensor Shield" plugged on an UNO like this "Sensor Shield (Version 5X) Separate 5V for Servos" This allows a separate power supply for servos and each servos can just plug in a 3-pin connector.
OR if you have a MEGA, the MEGA Sensor Shield also has separate servo power supply available.