This is an interesting and subtle question. You're testing a trading strategy, right? Presumably, it needs some time-series properties. If you do an independent bootstrap you'd mess those up.
At the same time, independent is good for looking at certain aspects (e.g., skewness over multiple horizons from a momentum strategy). Other than that, you'll probably need to consider a block bootstrap or other dependent bootstrap.
In its simplest form CBB (Circular Block Bootstrap)
- takes the data, lines up on a circle (to avoid endpoint problems), and
- For your blocksize N, you pick random starting points in the original dataset (on a circle)
- Fill in your bootstrap with the next N data points until your bootstrapped sample is the same size as the original.
Then run your strategy and calculate a Sharpe Ratio. From this, you can get a distribution of Sharpe ratios
The challenge is picking the right blocksize. Usually, this is done with reference to the autocorrelation function of the original timeseries.
For non-bootstrap statistics on Sharpe Ratios, Andy Lo has a paper called The Statistics of Sharpe Ratios, worth looking at. For IID, they are t-distributions. For non-IID, a HAC variance estimator is needed.