You can split up your scripts into files and "include" them with the source aka dot "." operator. The includes do not need to start with "#!/bin/bash", but they must either be in your PATH or have their PATH written exclusively in the main script.
Code:
#!/bin/bash
# A script that includes another script
source My_Other_Script.sh # include is in $PATH
source /path/to/the/include/My_Other_Other_Script.sh # explicit PATH