To visualise a bootstrapped paired Student's t-test, you can use R. You can use the boot package to perform the bootstrap and the ggplot2 package for visualisation. You can calculate the paired differences, perform bootstrap resampling, compute the mean difference for each sample, construct a bootstrap distribution, estimate the confidence interval, and plot the distribution with the marked confidence interval. The visualisation would typically include a histogram or density plot of the bootstrap distribution with the confidence interval highlighted.
A place to start would be to just visualize the original data, presumably some form of scatter-plot of test versus control. This would at least show why you are thinking of doing bootstrapping rather than a standard analysis.