BSL and ASL have different gramatical rules, but the modality is the same, so it's possible to understand the core of BSL better by studying ASL. At the moment, most papers about sign language grammars are explained at a linqustic level, as the resources are way skimpier than the major spoken languages. But as research advances, it will be easier to make systems and explainations that makes sense, more accesible for the average educated person. In english we have words like "nouns" and "verbs" and systems to understand english, used in normal language education.
At the moment, with so little resources available, in addition to the resources mentioned in this thread, it's an idea to speak with fluent users of the sign language you want to learn, and notice how they use identifiers, modifiers, localization and space. You can also find videos online clips to study. Also pay attention to how time is explained. Try to not focus on categorizing signs the same way as the spoken/written language you know, as it will confuse you more. Also try to find some high level sign language courses, like those deaf people and interpreters attend.
The way english grammars often is explained in school, with sentence structure with rules for words put here and there, verbs, nouns and so on is most of the time not transferable to sign language as the modality is totally different. So, learn what modifiers, localization and identifiers are, and forget the order of single words, verbs and nouns when using sign language 
And remember, a deaf person is not 100 percent bilingual before he/she knows two different sign languages
Hope this was helpful!
