"I am saying goodbye."
Translation:Mówię do widzenia.
Most of dictionaries only show some basic forms, that only indicate the model of conjugation (see mówić . Scans of an old, but probably the best to present dictionary are linked a bit lower on the previous page under "Słownik języka polskiego pod red. W. Doroszewskiego". If you click on the link, you will see the page mówić scanned from this noble dictionary, indicating the model VIa
All declension and conjugation tables may be found in Grammatical Dictionary of Polish - it contains over 450.000 words with all their grammatical forms.
Aaand... you may look for the conjugations of the most pupular verbs here: http://polishconjugation.com/ and here: http://www.tastingpoland.com/language/verb/verb_infinitives.html
Well, "jestem" does indeed mean "I am".
However, your mistake is interpreting "I am saying" as if it had two verbs. It only has one, it's a form of "to say". There is nothing about 'being' here. "I am saying" = "(Ja) mówię".
Over 99% of the Polish verbs has no distinction between what English distinguishes as Present Simple and Present Continuous. So "I say" and "I am saying" are translated exactly the same way.
Because Jestem is a verb. I found more information here: https://en.m.wikibooks.org/wiki/Polish/Conjugations_of_common_verbs