When you use “today morning I went to the bank”, you probably translated from your native language.
You shouldn’t use direct translation from your native language if you seriously want to improve.
In English, “today morning” is just redundant and unnecessary as we have “this morning” to indicate the morning that has just passed.
Your sentence construct is very unnatural. When you want to relate your morning activities to someone, or when asked you may say:
“I woke up late this morning. That caused me to miss the 7am bus and breakfast”.
If you need to start your sentence with “This morning….” you may try this construct:
“This morning while I was rushing to catch the 7am bus, I stubbed my toes on the door frame and they hurt like the hell. I woke up late hence the rush”.
When you start your sentence with “this morning….” you better have a more interesting story to tell than you waking up late which is merely making a statement.
Peace out guys.