In reply to Jill Wang.

1. Yes, the data should be linearly related if you are going to apply a linear regression model. You can graph the data to see if they are linearly related, or you can run a more formal hypothesis test. Passing and Bablok suggest a CUSUM test for perpendicular distances to the regression line. Thus, you have to compute the regression estimates (a,b) first, and the test is conditional on the estimates.
2. You are free to use a bootstrap CI if that makes you happy. I have not read EP09-A3, so I cannot comment on it. I do not know who wrote it or the theoretical basis for their recommendations.

PB discuss the CIs in Appendix 3. An assumption is that a certain quantity (which they call C) is normally distributed. You can prove that C is asymptotically normal, so for large data, the CIs are valid. PB did a simulation study for samples of size 40 <= n <= 60 and reported that "in all cases the actual confidence level is about 95%; it is never less than 91% or higher than 96%" (p. 719). They do not provide any information about samples with fewer than 40 observations. However, they note that "the actual level of the confidence interval for alpha is higher than 95%."

I can tell you that a bootstrap sample contains duplicate values for some pairs and omits other pairs. On average, a bootstrap sample omits 36.8% of the data, which means that you get a lot of duplicates. In the PB regression, "identical pairs of measurements with x_i=x_j and y_i=y_j do not contribute to the estimation of beta" (p. 711). The PB regression method excludes these duplicate values. Consequently, the average bootstrap sample discards 37% of the data. Thus, I would expect a bootstrap CI to be wider than necessary. Wide CIs means that you would accept the hypothesis that the measurement methods are equivalent more often than you should. Until someone shows me an argument that changes my mind, I do not recommend boostrap CIs.