@PepitoFiesta
First, congratulations! :-) Good luck with your new life in Bulgaria.
Usually, the residence application needs the same documents you used to get your D visa.
As far as I'm aware, there is no category of D visa based on "financial means", except perhaps the investment options (around 300k euros if I recall correctly). So I doubt the bank statement is a big deal, although it's obviously good to have.
I don't translate bank statements, and I don't believe it's necessary. They're just looking at the numbers,
If you're trying to show an amount in savings, you just need one statement showing your current balance. If you're trying to show income over a period, then you'd need statements reflecting the period (and income) asked for.
If you have money abroad, a statement printed off the internet is probably OK. The best is a bank-stamped statement issued by your local branch of a Bulgarian bank.
For context, the minimum wage here is just under 500 euros per month. If you can show savings to cover you for at least a year (i.e. 6k euros) and/or a pension approaching (or exceeding) this amount, this should be more than enough.
Usually, immigration offices are first-come, first-served, with plenty of folks standing in line. I typically try to get there at (or, preferably before) opening time. When you go depends on your tolerance for standing in line vs. your aversion to early mornings. :-) My local office (Plovdiv) has a ticket system, and I'd imagine most offices have implemented something similar. This means as soon as you get through the door, you get to this machine and get your ticket for your particular service (e.g. residence applications by non-EU citizens). Then wait until your number comes up.
You can go on your own, but I highly recommend getting a local "helper" or taking an interpreter/translator with you. My local interpreter charges me 50 leva for an hour, so that's the ballpark cost.
These are busy offices, so there are typically support services nearby. Again, my local in Plovdiv, has a row of shops just outside the entrance where you can get documents copied, or get help with translation, etc. I'd guess this will be pretty typical wherever you apply.
By coincidence, I am in the process of making a new residence application (family reunification) and I went over to Plovdiv immigration yesterday. The copy shop guy was absolutely fantastic: he went through my full application and verified that I had all the required documents. He pointed out which documents needed copies and made them. He spotted that I'd used the wrong application form, and told me to go ask for the correct one... which he then filled in for me (in Bulgarian, as they prefer). He also took me to the other shop to speak with the registered translator in order to get an official translation of the document he said required translation (a birth certificate). I'd be very surprised if you couldn't do something similar wherever you are.