We will assume that the parameters \beta follow a normal distribution. We can then define the confidence interval. Here we will be using as shorthands \mu_{\beta} for the above mean value and \sigma_{\beta} for the standard deviation. We have then a confidence interval
\left(\mu_{\beta}\pm \frac{z\sigma_{\beta}}{\sqrt{n}}\right),where z defines the level of certainty (or confidence). For a normal distribution typical parameters are z=2.576 which corresponds to a confidence of 99\% while z=1.96 corresponds to a confidence of 95\% . A confidence level of 95\% is commonly used and it is normally referred to as a two-sigmas confidence level, that is we approximate z\approx 2 .
For more discussions of confidence intervals (and in particular linked with a discussion of the bootstrap method), see chapter 5 of the textbook by Davison on the Bootstrap Methods and their Applications
In this text you will also find an in-depth discussion of the Bootstrap method, why it works and various theorems related to it.