The SDE for a Bessel-3D bridge between $(x,t) = (0,0)$ and $(x,t)=(0,T)$ (starts and ends at the origin) is given by $$dX_t = \left(\frac{1}{X_t}-\frac{X_t}{T-t}\right)dt + dB_t$$ where $B_t$ is a Gaussian process. Now I have the following SDE: $$dX_t = \left(\frac{1}{X_t}-\frac{X_t}{T-t}+a\right)dt + dB_t$$ where $a$ is a constant.
Could I interpret the later as a SDE for a Bessel-3D bridge? How can I transform from the later SDE to the former?