Barriss’s actions were motivated by her own sincere belief that the Jedi Order had fallen. She thought that the Jedi had become pawns of the Dark Side themselves:
BARRISS: Because I’ve come to realize what many people in the Republic have
come to realize, that the Jedi are the ones responsible for this War.
That we’ve so lost our way that we have become villains in this
conflict, that we are the ones that should be put on trial, all of us!
And my attack on the Temple was an attack on what the Jedi have
become: an army fighting for the Dark Side, fallen from the Light that
we once held so dear.
Unlike Count Dooku, who used insinuations about the Republic’s corruption in an attempt to sway Obi-Wan to the Dark Side, Barriss was acting out of genuine conviction. She may even had a point: the Jedi had accepted a clone army of dubious freedom, engaged in constant bloodshed, tried to employ assassination, and, in the end, were fighting for a Republic led by a Sith Lord.
Even Ahsoka Tano, whom Barriss had tried to frame for her own crimes, admitted as much, and with the benefit of hindsight. She even thought that if Barriss had been heeded, the Order might have had a chance of stopping Palpatine:
“Barriss Offee was wrong about a lot of things. She let her anger
cloud her judgment and she tried to justify her actions without
considering their wider effects. She was afraid of the war and she
didn’t trust people she should have listened to. But she had a point
about the Republic and the Jedi. There was something wrong with them,
and we were too locked into our traditions to see what it was. Barriss
should have done something else. She shouldn’t have killed anyone, and
she definitely shouldn’t have framed me for it, but if we’d listened
to her—really listened—we might have been able to stop Palpatine
before he took power.”
Also, when Ki-Adi-Mundi mentions her, he describes her as "a Separatist terrorist.”
“We weathered a storm such as this poorly with the treachery of Barriss
Offee. None of us could have imagined such a seemingly ideal Padawan
turning into a Separatist terrorist.”
Surely if she had fallen to the Dark Side, he wouldn’t have described her as “turning into a Separatist terrorist.” He’d just say “falling to the Dark Side.”
With all this in mind, I’d say that she certainly did not fall to the Dark Side. On the contrary, she was trying to fight against it. She did not cause suffering for the sake of it, nor did she let her passions rule her. Nor did she seek to dominate others. Had she truly fallen to the Dark Side, she would not have spent her last few seconds out of jail trying to convince people that the Jedi had been corrupted.
That said, I do think she was tempted by the Dark Side.
There’s two pieces of evidence. First, in the previous quote Ahsoka describes Barriss as letting “anger cloud her judgment.” Whenever a Jedi lets themselves be influenced by anger to such an extent, they are in danger of being influenced by the Dark Side. Being so angry that one kills innocents…this surely is enough to be tempted by the Dark Side. It is for Anakin, anyway.
The other bit of evidence is this dialogue:
ANAKIN: Funny. Those belonged to Ventress. You should have gotten rid
BARRISS: I think they suit me.
Fighting with red lightsabers is no sign of the Dark Side. Obi-Wan once borrowed one of Ventress’s lightsabers, for example. But purposely taking them and keeping them? Keeping them in one’s room, when one has a lightsaber of one’s own? Keeping them even though, as Anakin says, it would have been smarter to get rid of them? And then she says that they “suit her.” I can’t imagine that she was talking about red being her favorite color. I think she kept the lightsabers because she was feeling some degree of attraction to what they represented: the Dark Side.