Was Portia really angry with Bassanio when she discovered he had given away the ring? What was Bassanio's explanation for what he did?

No, Portia was surprised he gave away the ring, but she wasn't angry.

In Act V, Scene I, Nerissa demands that Graziano show her the ring he gave away to Portia's "clerk" in Venice. They start to argue over it, with Graziano defending his action as a form of kindness for Antonio. Portia overhears them and pretends to "discover" what happened. She then demands that Bassanio show her his ring, which he of course cannot do. Portia and Nerissa then berate their husbands for giving away the rings, and even tell them that they would prefer to sleep with the doctor and his clerk rather than with their unfaithful husbands.

Antonio offers his assurance that neither Bassanio nor Graziano will ever give away their wives' gifts again. Portia thanks him and asks him to give Bassanio another ring to keep. Bassanio looks at the ring and recognizes it as being the same ring he gave away. Portia then tells him that the doctor came back to Belmont and slept with her. Bassanio is amazed and does not know how to respond.