In Dark Souls, there is an acceleration time while running where the character accelerates from standstill to walking, and from walking to sprinting. This means that after inputting these movement changes it takes time for the character to reach the full speed of the respective animation.
Differences Between Male and Female Acceleration
Skipping the Acceleration Time
Male characters accelerate and decelerate slower, this means they have a speed disadvantage when sprinting but they are at an advantage when going back to regular speed. However blending some top body animations into the mix, you can give the female acceleration to the male animation. This is usually achieved by toggling your equipped weapon slot (d-pad left/right) at the right time. Usually you have to start mashing a bit after you start holding your sprint button.
Note this doesn't work with every weapons but the routes you can find around usually use such weapons anyway.
Alternatively (since you will most likely have a bow), you can achieve the same result by switching between ammo type (even if you only have the one) by mashing L2/R2.