Double bootstrap or 2 separated bootstraps to estimate the standard error?

Question

I want to estimate the standard error of an estimate.

It depends on the rows and columns of a dataframe.

Two possibilities:

• Make a bootstrap on the rows to estimate $se_{row}$.

  Do the same with the columns to estimate $se_{col}$.

  Then take the general standard error is $se_{tot} = \sqrt{se_{row}^2 + se_{col}^2}$

• Do a double bootstrap on the rows and columns, and get the standard error this way

Which one is more sound ?

For info, the rows are items' difficulties and columns are judges.