There is no limit to the number of messages that you can send to the service bus. This depends upon the message size of the individual messages that you are sending per call and the batch size that you have set in your application.
Let's take an example you have created a standard SKU of service bus and using the batch operation to send the messages. The batch size you have set is 10.
So the number of messages will depend on the size of each message and the batch size that you have defined.
For standard SKU, message size limits to 256 KB including header and message content. So if your each message size is 50KB then your application will only send 5 messages (50*5 = 250 KB) per call despite the batch size that you have set. If your message size is 10KB then your application will only send 10 messages (10*10 = 100 KB) as the batch size limit has reached that was set by your application.
Hope the above helps. Please let me know if you have any queries.
Please 'Accept as answer' and ‘Upvote’ if it helped so that it can help others in the community looking for help on similar topics.