Delta Method for estimating the variance associated with each class in an ordinal regression model

Question

I have an ordinal regression model which predicts an ordinal response variable ranging from 1 to 9.

Can the Delta Method be appropriately applied to estimate the variance of my model's output? (the probabilities associated with each class). If so, What factors should guide my decision on the sample size for optimal results?

I've been exploring various methods to estimate the variance of my model's output and came across:

1. Bootstrapping
2. Delta Method
3. Bayesian methods like Markov Chain Monte Carlo (MCMC)