As noted, how much you fish is key. Also, how fast you fish. Running on the assumption that you only ever do full 18 item buckets:
You would take ~4,167 buckets to get the Angelic Rod, or 8,334 buckets to unlock the Angelic Plus.
Assuming you take 6 minutes to finish each bucket, that's 25,002 minutes (416.7 hours) for the Angelic Rod, or 49,998 (833.3 hours) for the Angelic Plus. That's ~17.36 days and ~34.72 days respectively, of nonstop fishing time.
If your goal is about a year, assuming that you fished every day:
It would take about 1.14 hours of fishing per day to get the Angelic Rod, or 2.28 hours of fishing per day to get the Angelic Plus.
If you fish faster, which doesn't happen that much faster legit, or slower, these numbers change of course. So does the fact that the captcha is currently the equivalent of a turd, but it is what it is. Usually going for trophies is a good way to make headway on this particular goal. When I was still keeping up with scores properly and competing myself, doing about 1,000 buckets a month was pretty standard for upper top 10 scores (not record attempts and stuff, just standard runs). That would mean you could get the Angelic Rod in about 4 months, and the Plus in about 8. It all just kind of depends on how dedicated you're willing to be to the cause.