I don't think a hole this long is possible with any conventional drill bit, and finding a suitable one of this length which would be difficult to say the least. And anyway there is a significant problem with drift or wander, particularly when drilling into end grain as you might be here. Note: this is even if the drilling is done on a drill press, the amount of wander can be quite amazing.
Even in the past when very long drill bits were more commonly seen as part of the woodworking tool kit (either augers to be turned directly with a wooden handle, or for use with a brace) once you got to very long lengths in relation to the diameter of the hole it was common to use specialist bits made for that purpose only, for example shell bits.
Here's a modern shell auger to give an idea of what the traditional style looks like:
I suspect the only way you'll achieve this length of hole is if you can find a suitable shell auger bit or are willing to go to the trouble of making your own. You'd start the hole with a normal bit or matching diameter, then slip the shell bit into the hole and continue from there.