I don't know of any repositories that will provide you with BASH 4.3 for Amazon Linux.
If you have a specific requirement for this version of BASH then you're probably going to have to compile it from source, if you've no experience in doing that then this could be quite technical, there are some instructions on this over at the BASH FAQ; ftp://ftp.cwru.edu/pub/bash/FAQ.
Is there a specific reason that you need BASH 4.3? I'd be interested to hear it if so.
UPDATE: I've just spun up an Amazon EC2 instance running the latest version of Amazon Linux and upgraded bash by compiling from source. There was no dependency issues and everything worked as expected for me.
Download the latest package from http://ftp.gnu.org/gnu/bash/bash-4.3.tar.gz and follow the install instructions from http://www.linuxfromscratch.org/lfs/view/development/chapter06/bash.html. Once done I rebooted the system and it booted fine using the new version of bash. I tried running a couple of scripts I had laying around which worked with older versions of BASH and they appear fine.
Obviously if this is a production system please test on a dev/staging/test environment first!