I have always thought you subtracted the AC from the THAC0 thus getting the goal number for the roll. The bonuses (usually not being that impressive) only need to be considered if you failed but got really close.
So this seems to speak to the assumption that everyone "back in the day" knew what "number" they were aiming for on the d20 roll after applying math.
That wasn't the way it worked in most groups I played with at all - the conversation generally went something like the below:
1. Player rolls a d20. Let us assume for the sake of argument a "15" was rolled (situational modifiers like called shots could come into play at this point as they do in modern games).
2. Player consults his character sheet with his "base" precalculated THAC0. Let us say for the sake of argument his THAC0 was 19 (first level character).
3. Player does the math of subtracting "roll result" from "THAC0" (in this case, the math operation is 19-15).
4. Player announces, "I hit Armor Class 4" (implied: or worse)
5. DM compares the announced Armor Class hit with the target AC. If the target AC is equal to or higher than the number announced, the DM responds "that's a hit/miss"
Compare to modern games:
1. Player rolls a d20. Situational modifiers can come into play at this point as they did in step 1 before.
2. Player adds all "permanent" modifiers to his roll (probably pre-calculated with BAB/Proficiency, Attribute Bonus, etc.). For the sake of similarity, let us assume these are "0."
3. Player announces "I rolled a 15" (or if you prefer, "I hit Armor Class 15 or worse")
4. DM compares the announced Armor Class with the target AC. If the roll is equal to or higher than the Target AC, the DM responds, "that's a hit/miss."
There IS an extra step in THAC0 (subtracting the rolled result from THAC0) but IMO subtraction is a fairly trivial mathematical operation (YMMV), so I will cede it is "more complex" but I wouldn't call it "much more complex."
The difference is in the DM comparison step wherein the DM compares "which number is higher" - in THAC0 systems, if the AC is higher it's a hit, in d20 systems, if the roll is higher it's a hit. But as mentioned upstream, this is essentially the same operation ("comparison") and once you learn which way to compare, either system makes sense.