Travel Coffee Mugs Dishwasher Safe

Can you clean a plastic Coffee Travel Mug with baking soda?

I have a metal water bottle that says to clean it that way, and it works great… I need a better way to clean my plastic coffee travel mug as I cannot find one w/ metal inside, so mines not dishwasher-safe.
I have to soak it for awhile to get the coffee smell out when I want to use it for tea, and and my dish detergent makes it smell like lemon!
Would baking soda get the odors out or just make it taste gross?

I have the answer for this…
DENTURE TABS I swear! Those little discs clean EVERYTHING! you may need to use four or five.
You would not believe what those things clean! I use them in my travel Cups all the time!
Fill with hot tap water dump in the tabs. wait ten minutes or let soak all night, wash as normal.. you will be shocked at how well it works. and ANY brand will do it… so buy cheap!