How to set bash aliases for docker containers in Dockerfile?

Basically like you always do, by adding it to the user's .bashrc:

FROM foo
RUN echo 'alias hi="echo hello"' >> ~/.bashrc

As usual this will only work for interactive shells:

docker build -t test .
docker run -it --rm --entrypoint /bin/bash test hi
/bin/bash: hi: No such file or directory
docker run -it --rm test bash
$ hi
hello

For non-interactive shells you should create a small script and put it in your path, i.e.:

RUN echo -e '#!/bin/bash\necho hello' > /usr/bin/hi && \
    chmod +x /usr/bin/hi

If your alias uses parameters (ie. hi Jim -> hello Jim), just add "$@":

RUN echo -e '#!/bin/bash\necho hello "$@"' > /usr/bin/hi && \
    chmod +x /usr/bin/hi

To create an alias of an existing command, might also use ln -s:

ln -s $(which <existing_command>) /usr/bin/<my_command>

If you want to use aliases just in Dockerfile, but not inside container then the shortest way is ENV declaration:

ENV update='apt-get update -qq'
ENV install='apt-get install -qq'

RUN $update && $install apt-utils \
    curl \
    gnupg \
    python3.6

And for use in container the way like already described:

 RUN printf '#!/bin/bash \n $(which apt-get) install -qq $@' > /usr/bin/install
 RUN chmod +x /usr/bin/install

Most of the time I use aliases just on building stage and do not go inside containers, so first example is quicker, clearer and simpler for every day use.