Hi there, if I may make a suggestion
you can compress it down to a smaller size/bitrate, so that it is easier to upload to places like YouTube.
Myself, I record with the Motion JPEG codec, since it's easier to edit, then when I'm done, I render out the video to something smaller like MPEG-4/AVC or WMV, then the size is usually down from gigabytes to less than one gigabyte and I let that upload while I go do something else.
AVI is the type of container, and inside it can have many different formats, which is why it usually ends up being an AVI file in the end, with Bandicam. If you don't mind a bit lower quality, try recording in a lower bitrate to keep the size down, or compress it before you upload with a free program like WIndows Movie Maker (if you use Windows) or Virtualdub or Avidemux. Kino or Kdenlive or WinFF are some Linux programs you can use (WinFF works in Windows as well). Nero, Sony's Vegas and many more pay programs also offer conversion to different formats and lower filesize if you don't mind lowering the bitrate or quality.
You can also record in Bandicam in a format that compresses more, like MPEG-1/Xvid with lower the bitrate, or MJPEG with a lower quality setting, but these might become too low quality for you. It depends on the type of recording you are making (game, screencast, etc) and what looks "good enough" for you in the end. Do some tests with a few programs and see which ones make your files smaller while still looking "good enough" to you.
Good luck with it and have fun