I got much further last time I played Scarlet Devil when I started religiously using up all my bombs, it was the first time I managed to get up to Remilia. I haven't played touhou since then however. My advice to get further for noobs is to get into the habit of being bomb-happy, then gradually dial that back.
Eeh, if you want to get deeper in for the short run, sure. But I distinctly remember my own experience being that I started to git gud (not that I am, I can't no-continue any of the games on higher difficulties still) when I stopped using bombs as a crutch -- that is, there are times where you should absolutely spam them, but using them as a mulligan when you should have been able to avoid a death on your own just lets the bad habits stick around.
When I had more practice, I would generally only bomb after death. I'd still try for a lucky escape, but be prepared to sacrifice a bomb rather than a life on the death-sound.
I may be overestimating my previous skill, though
I just did a run, rusty, and got past the Prismriver sisters despite losing a couple of lives in stage 2. Died to the half-ghost wolf with the katana, which is as far as I remember getting without continues anyway.
You fight Lily White(the angel-thing) before the Prismriver sisters.
EDIT: ...I just came up with a crossover idea, Sakuya is almost certainly related to either Corvo or Daud from Dishonored. All three are knife freaks that can bend time.
Oh yeah, oops. Got confused since she doesn't talk, and she's harder than the sisters! At least to me. I assumed she was midboss of the next stage... Which I guess doesn't have a midboss, just wolf-ghost and a lot of obscenely difficult fairies.
Also I like that theory, lol.