This really depends on how complex of a chatbot is being developed. A simple QnA chatbot is relatively inexpensive and if deployed on the F0 or Free tier then your cost would be well under $100.00 a month.
However, if you use the Virtual Assistant framework to develop a full blown virtual assistant then you could see a significantly higher charge.
Links to the Azure Pricing calculator are below to assist you in developing an estimate for the cost of your chatbot.
https://azure.microsoft.com/en-us/pricing/calculator/
If you are interested in the Azure virtual assistant framework the link to the overview and tutorials are below.
I hope this helps.