H bridge dc motor and servo motor

Hello
I had recently made a circuit on an Arduino Uno that contains an H bridge and a dc motor that can be spinned in both ways (nothing spectacular). Now i've replaced the DC motor with a servo motor and then the problem occured: it only works in one direction (the normal one when the tension is positive from + to -). I am sorry if I really ask a stupid question but i want to know if all servos have this one direction tension (making the H bridge useless) and if I can make the circuit without the bridge, the direction being implemented only in the code.
Thanks.

Also the links of my ideas
https://circuits.io/circuits/2514119-the-unnamed-circuit with the bridge

https://circuits.io/circuits/2508180-the-unnamed-circuit and without the bridge

You should not reverse the supply polarity on a standard R/C servo.

I understand, so the remaining posibilities are to use a non-standard servo(?) or cut the H bridge and control the motor's direction by code ( like angle++ or angle -- ) ?

If all you want is servo control, then use the Servo library and ditch the H-bridge - the servo has got its own

Another point - generally it's not a good idea to power the servo from the Arduino's 5V supply. You might get away with it with a low-power "micro" servo, but not with a standard one.
And even with a "micro" servo, it could potentially put spikes on the 5V supply rail and cause problems. You really need a separate supply for the servo.

Is this a continuous-rotation servo?

All hobby servos consist of an internal H-bridge, angle sensor and feedback loop driving the H-bridge.
In other words it is a self-contain motor driver and control system.