Can I change the size of the bot on my site?

Yes!
The default widget for bots is 370 pixels by 590 pixels. Technically you can change this size via custom CSS, however, modifying widget size may affect other elements in the chat unexpectedly so it may require some finessing.
In the Bot Management tab, at the bottom of your "Appearance" settings, you will find a file uploader to add your CSS file. Uploading this file will overwrite Instabot's settings and apply the settings from the file.
Please note that only accounts on the Standard plan and above can upload a custom CSS file.

13831383

Upload a CSS file