What is the shortest type of text encryption? I have the following text that I want to encrypt with a password:

"This is my secret password: 1234567890"

encrypted with AES:

SgAHzFc3vluxLqZuzZKg8dzhy918N41SUU1BfBXN8CoEDfVJ0R9hox8PT2jKYA==

pass: 12345

When I encrypt this with a password using AES, the encrypted string is 64 characters.

Is there another type of encryption that is less than 64 characters? Or maybe there is an encryption that also compresses the encrypted string?
You don't say what mode of operation you are using with AES. The mode of operation can have a big impact on the ciphertext expansion. There are streaming modes, such as CTR, for which the ciphertext will be the same size as the plaintext. For these modes (an pretty much any mode you would want to use in practice) you will also have to transmit a nonce or IV in addition to the ciphertext.

One thing you should be aware of is that modes like CTR are malleable, which is a huge security issues. So, I highly recommend you use authenticated encryption so that you don't have these security issues. This could be done by computing an HMAC over the ciphertext or using an authenticated mode.