Normally, there is a Connector Service between the client and a bot. It is possible to bypass the connector services, and post directly to the bot but there are a few things to keep in mind. One of the issues you will run into is the activity.ServiceUrl is expected to be the callback base url for return messages: ref BotFrameworkAdapter#L843 Without a valid ServiceUrl, bot replies will all end in exceptions, since there is no valid place to send the responses. You can setup a MockChannel to receive these bot replies. Once it is setup, just ensure your ServiceUrl of the message sent to the bot is pointing to that MockChannel.
Sometimes I use the Emulator's Connector Service with PostMan. This can be done without having a MicrosoftAppId and MicrosoftAppPassword. You'll see the endpoint the Emulator Connector Service is listening on within the Log when you open a Live Chat tab:

This would then be the baseurl to use for PostMan.
Create Conversation:
(note: the emulator expects an Authorization header with a Bearer token, but the value does not matter since we aren't using a MicrosoftAppId and MicrosoftAppPassword)

Post Message:

Get Messages:
