In case anybody comes looking for this answer. I found a fantastically thorough solution to integrating Contact Form 7 with Bootstrap 3. Just add these lines to your forms.less file or theme.less file and recompile Bootstrap.
input[type="text"].wpcf7-form-control,
input[type="password"].wpcf7-form-control,
input[type="datetime"].wpcf7-form-control,
input[type="datetime-local"].wpcf7-form-control,
input[type="date"].wpcf7-form-control,
input[type="month"].wpcf7-form-control,
input[type="time"].wpcf7-form-control,
input[type="week"].wpcf7-form-control,
input[type="number"].wpcf7-form-control,
input[type="email"].wpcf7-form-control,
input[type="url"].wpcf7-form-control,
input[type="search"].wpcf7-form-control,
input[type="tel"].wpcf7-form-control,
input[type="color"].wpcf7-form-control,
select.wpcf7-form-control
{
.form-control
}
.wpcf7-checkbox .wpcf7-list-item
{
.checkbox
}
.wpcf7-checkbox.checkbox-inline .wpcf7-list-item
{
.checkbox-inline
}
.wpcf7-radio .wpcf7-list-item
{
.radio
}
.wpcf7-radio.radio-inline .wpcf7-list-item
{
.radio-inline
}
Then, recompile bootstrap using a command like this:
lessc -x bootstrap.less > path/to/my/folder/bootstrap.min.css
I hope this helps someone.