The bootstrap method is only useful if your sample follows more or less the same distribution as the original population. In order to be certain this is the case, you need to make your sample size large enough. Keep increasing the size until you get convergence and obtain unbiased estimates or standard errors . No one number fits all problems, but > 500 should do it! :)

Check the answer to this question. You might find it helpful. https://stats.stackexchange.com/questions/33300/determining-sample-size-necessary-for-bootstrap-method-proposed-method

@ Thanks Andrew and Mum Taggu for the response.