I am not an accountant (my business partner is) but this is how I think about it:
(Revenue - Cost of Goods)-(Operating Expenses)= Operating Profit.
And then it becomes tricky, fancy and artsy. This is where the accountants come in.
Operating Profit - BlackBox [see note] = EBITA (earnings before the deduction of interest, tax and amortization expenses)
EBITA - (interest, tax, amortization) = Earnings (aka: Left over and available for owners.)
The timeframe of the calculations is essential for understanding the health of the company. The most common are quarterly tracking and annual reports.
The examples in your question of having a bank account full of "salaried and expenses for 3 months with running profits" says something about the cash position of the company. There are companies that are profitable with a poor cash position, and companies that are not profitable with a very good cash position.
The indicators of cash position as mentioned are important to assessing the overall health of the company but not necessarily the profitability.
As the sole owner -- seeking to understand if you are profitable -- you need to be working closely with your accountant. You need to have a good financial statement template. You need to make sure that all income and expenses are being posted in your accounting software. Then you need to make sure that you are getting reports from this accounting software on a regular basis (weekly, monthly, quarterly).
These reports need to provide you the information to track income, expenses, costs, and the bottom line. You need to be tracking not only sales coming in -- but the resulting gross margin those sales. You need to make sure that it doesn't cost you more to provide your product/service then you receive from it. "Managing toward top line revenue" means watching only he money coming in. That will kill you as a owner.
You then need to track your operating expenses. Obviously you are trying to keep them low. Hold down overhead costs. You can then watch your EBITA number. That EBITA margin will give you a good tracking indicator of profitability.
Note: I am sure there is a simpler way to explain it without as many acroynmns and without the "black box" of "Wherever they can get away with putting in here legally"