To be clear you are asking about covering the Torah while saying the blessings (and not at any other time).
SA O Ch 139 (4) says:
Everybody who reads (should) bless before it and after it. They should
open the Torah scroll before they bless and see the verse they need to
start with and then they bless and then read the Torah and then roll
it up and bless (the second blessing). Gloss: and at the time that
they bless the first blessing they should turn their heads to the side
so that it does not appear that they are reading the blessing from the
Torah (The Kol Bo) and it seems to me that they should turn to the
On the words “and then they bless” Mishna Berura says:
ר"ל שאין צריך לגלול הס"ת בשעת ברכתו וליכא למיחש שמא יאמרו ברכות כתובות
That means that there is no need to roll the sefer closed at the time
of his blessing and one does not need to suspect that people will say
that the blessings are written in the Torah
but for the blessing after the reading the Mishna Berura says that the sefer should be closed up.
The Biur Halocho says:
ודע שיש פוסקים שסוברים דאם רוצה לגלול ואח"כ לברך עדיף טפי אלא דהלכה
כר' יהודה שאינו מחוייב לעשות כן ועפ"ז נוהגין איזה מקומות שרואין
וגוללין ואח"כ מברכין ונהרא נהרא ופשטיה [אחרונים]:
and you should know that there are poskim who hold that it is better
if one closes the sefer and then makes the first blessings. But the
halocho is like Rebbi Yehudah that one is not obliged to do this. Thus
some places have the custom to close the sefer before making the
blessings and every place should follow its own custom.
It is thus clear that there is no requirement to cover the sefer during the blessings before the reading and the main law is that the sefer does not even need to be rolled closed during the first blessings.
I have no source for whether or not to cover the sefer for the concluding blessing.