While Jackson and Co. Didn’t pull out all the stops to show time passing, they very much go out of their way to stay faithful to the written word where possible.
It seems like maybe a few weeks or months perhaps pass, if you don’t think “horses and riding to different countries is going to take longer than cars and going a few towns over/the next state” then you could think it was a few days.
All that said, Yes, I also would have liked to encounter Tom Bombadil but ultimately he is meaningless to the overall story, and would just slow down an already long movie. I would definitely watch a 5 hour cut of every part, but not very many people would.
I just pulled up the extended edition and rewatched, the entirety of “keep it secret, keep it safe” to “is it secret? Is it safe?” and those 17 years was 31:50 ish in to 36:40ish. So about 5 minutes of screen time and most of that was Gandalf travelling to/researching in minas tirith, and Frodo and the Gang having a mug at the green dragon. Given the time of year, the fact that things “look chilly” in the outside establishing shot could be taken to mean “same time of year, maybe not much time has passed”
Apogies for the keyboard vomit, I don’t get to nerd out on LOTR often.
Go punt kick the first fish back into the ocean as it tries to waddle it’s fat ass out of the water.
I know that’s not how evolution works but I can dream… Life would likely be vastly different given such a long period of time with something like that changing either way.