Searching for subtitles specifically matched to the release is best done through dedicated subtitle repositories. These sites provide .srt files that are synchronized for the timing of high-definition BluRay rips. Where to Find Subtitles
If you find the subtitles are slightly off-sync (a common issue even with BluRay versions), most media players allow you to adjust the timing on the fly: subtitle Meet.Me.In.St.Louis.1944.1080p.BluRay....
: A massive database where you can filter results specifically for 1080p BluRay releases. Searching for subtitles specifically matched to the release