It is unclear as to the depth and diameter, from the description it sounds like you want to start at 3/4" with a final diameter of 3" or is that the depth? As others have mentioned, you are limited by the boring bar diameter and material as to the depth of a hole that you can bore. There are some variants of steel, that can bore slightly deeper than standard steel boring bar, heavy metal and carbide boring bars. I prefer indexible type as you can change the insert specific to the material. The boring bar insert seat can be negative, neutral or positive rake. I typically use CCMT /CCGT neutral or CPMT/CPGT positive rake insert boring bars. You get less chatter, and I tend to use a sharper ground edge insert for softer materials with a bigger nose profile. Keep you boring bar clamped in the holder as short as possible, least amount hang out.
If you desired to bore to a larger diameter, then I suggest you look into at least 2 boring bars, a 5/8" and a larger 1". Both can take the same insert, so something like a CCGT 32.52 insert. Using a 1" boring bar, you should be able to bore a hole to a depth of 3-4", carbide probably 7". Carbide is much more expensive then a good steel boring bar, like 8-10X. They are also brittle and can snap easily. Really need an assortment of sizes, and maybe 2-3 types of inserts. I routinely turned/bored bearing bronze, it can be prone to chatter. I choke up on the boring bar, and recently purchased a used 1" carbide boring bar which works well. Also a larger nose profile will give a smoother surface, but need you need to take a deep enough cut so it shaves the material as opposed to pushes the material. So one last approach to boring smaller holes with a lathe is to drill out most of the material, and then do the final sizing with a 3 or 4 flute end mill. I use an ER40 holder so can accommodate up to a 1" end mill.