How to append code verbatim to .bashrc?

I'd suggest a here document

$ cat >> .bashrc <<'EOF'
export PATH="/home/user/.pyenv/bin:$PATH"
eval "$(pyenv init -)"
eval "$(pyenv virtualenv-init -)"
EOF

So long as the EOF word (which can be anything) is quoted, no shell expansion of the body takes place.

However, the usual echo '..' >> ~/.bashrc will evaluate the statements before appending. How do you properly append such statements to a file using the command line without evaluation?

No it won't. Anything inside of single-quotes is completely un-evaluated. You can use
echo 'eval "$(pyenv virtualenv-init -)"' >> ~/.bashrc without any worry that anything will be interpreted. The only character of any significance in a single-quoted string is a single-quote (which ends the string, and cannot be escaped.)

You can add \ in front of special characters.

For example:

echo export PATH=\"/home/user/.pyenv/bin:\$PATH\"

gives the following result:

export PATH="/home/user/.pyenv/bin:$PATH"

so the quotation marks and the $PATH are still there.