Where to begin with 'Bride of Frankenstein'? Well, preferably at the beginning and repeatedly. It remains one of the outstanding contributions to gothic horror cinema and one of the most lucidly realised in any era. It also has several very interesting things to say. Is it far? No. But you may want to bring a coat.
The key development the film brings is, of course, the addition of the Bride herself - and this is really the key element of the movie. It has it's roots in a sub-plot of Mary Shelley's novel, where it is suggested to Frankenstein that the monster should have a female companion. This is of course expounded at length in the film where it is envisaged that the monster should be built a companion as the next stage in Frankenstein and Pretorius' 'grand collaboration'. The notion of the monster and the Bride as some pseudo-Biblical couple is clear, as is the Bride as some kind of sci-fi-age Eve. In Shelley's novel there were fears that the monster and his (uncreated) companion would breed and populate the world with monsters - which is rather the point.
A certain ambiguity also runs through the film, from the title down - the 'bride of Frankenstein' is, after all, actually Elizabeth and not the Bride-monster, and it is Elizabeth who provides the moral centre of the film. Henry is flaky, vainglorious and prone to destructive bouts of megalomania - it doesn't really take much pressure from Prestorious to get him back in scrubs - and he ignores Elizabeth's not entirely unreasonable advice throughout the film. There is also a strange symmetry to the simultaneous abduction of Elizabeth and the creation of the Bride, introduced (rather pre-emptively) by Pretorius as 'the Bride of Frankenstein!' It's almost as if Frankenstein's old mentor is trying to set him up with his new creation.
But the real core of the film is the attitude of the female characters. Even in the introduction Byron rather blithely suggests that Mary Shelley is 'an angel', prompting the author to reply 'you think so?' - suggesting a certain defiance beneath a polite smile. Such independence is also transplanted to the Bride (both parts, crucially, played by Elsa Lanchester) who gives the whole film it's killer punchline in the last ten minutes.
After her creation for the sole purpose of providing companionship to someone else, with no indication that her creators expected her to have or use any sense of agency, the Bride nonetheless thinks for herself and takes ownership of the only decision she is able to make - her relationship with the monster. And with that decision she chose to be true to herself and reject him.
Which just goes to show that the old sayings are true: you can make a woman out of bits of women you find in graves, but you can't make her fall in love with a man you've built from bits of men you found in graves.