Do entropy changes have an equivalent of bond enthalpy?
Please note that you are calculating the $\Delta U$ with your bond breaking/forming method. If there is low volume work done, then you can approximate:
$$
\Delta U \approx \Delta H
$$

For the entropy: Yes and no. I have no idea for liquids but qualitatively I would guess that it is not possible to have a quick and dirty method as you wish for this phase. And even for gases and solids it is quite a long work.

For gases you can calculate the entropy for every component itself and then add/substract.

Translational (Sackur-Tetrode):
$$
S_\text{trans}= R \ln \left( (2\pi m k_B T)^\frac{3}{2} \frac{V_m}{N_lh^3} \exp(5/2) \right)
$$

Rotational:
$$
S_\text{rot}=R\left(\ln\left(\frac T\Theta_\text{rot} \right) +1 \right)
$$

Vibrational:
$$
S_\text{vib}=R \left(\frac{\Theta_\text{vib}}{T} \frac{1}{\exp\left( \frac{\Theta_\text{vib}}{T}\right)-1} - \ln \left(1-\exp\left( \frac{-\Theta_\text{vib}}{T}\right) \right)\right)
$$

For solids you could calculate the heat capacity $C_p(T)$ with the Debye modell and then integrate from 0K.

I am really sorry, but I do not think, that there are easier methods.