"check the GSM character map for SMS and if it is, say 64 characters, I can use 6 bits for a character."

It is, I believe, 7-bit - and GSM provides a means to stuff one-and-one-seventh characters into each Octet.
Check the GSM specs.

Of course, if you can further restrict the character set, you could do your own "packing" - like the old DEC Radix-50 which, IIRC, packed three characters into 2 bytes?

For such small messages as GSM SMS, I'd be suspicious that the overhead of something like PKZip wouldn't be worth it.
But that's purely a guess!