Without homebrew material or a very accommodating DM, you cannot. Let's look at the options...
Not available until 7th level. Only RAW work-around is to get your hands on a Wand of Polymorph.
As you mentioned, you cannot turn into something with a Flying speed until level 8. This is out.
Become a creature like a Vampire
This requires explicit permission from your DM and WILL greatly upset the party balance. Also, there is a strong precedent in the rulebooks for a DM to take control of any PC that becomes an evil creature. (ex: MM207, 295; CoS191, 196)
Get a Cloak of the Bat
Rare magic item that lets you turn into a bat once per day...and also fly while in dim light or darkness.
If you are dead-set on this idea...you can try talking to your DM about homebrewing up an item that can let you do this. Perhaps a broach that lets you turn into a bat x-times per day or something. This is fully within your DM's control, though...so I can't give you a RAW response.
Alternative: Bat Familiar?
If you want to 'be' a bat without actually turning into one...perhaps you could roll a Wizard, snag Find Familiar, and summon yourself a bat? You can hop into the head of your familiar and drive them around on remote control--so you could 'become' a bat in the sense of inhabiting the body of one, while your real body sat back and relaxed. Warning: limited range.