Yes, they are both OK.

Yes.....but they aren't equivalent. The standard, neutral statements are these: Singular: There isn't a bridge Plural: There aren't any bridges. You'd use the first (singular verb, a/an, singular noun) when you might expect there to be one bridge, and you'd use the second (plural verb, 'any', plural noun) when you might expect there to be several bridges. The construction with 'any' and a singular countable noun is more unusual, and it is mainly used to add emphasis, particularly in conversation. For example: "At the end of a long road, you'll see a bridge. Cross the bridge, and then..." "Wait a moment. Look at this map. See? There isn't any bridge!" "You're right!That's strange. " Like "There is no bridge", it can be used to show surprise or annoyance, to contradict a assumption (as above), or to add weight to the statement. If I were you, Helen, I wouldn't teach the "any+singular countable noun" construction to your students unless they are very advanced. In 99% of cases where foreign learners use this construction, it is actually a mistake. Chinese learners struggle enough with articles and determiners, and teaching them an emphatic construction which seems to go against the rules will do them no good at all! Just stick to the two standard constructions.

Generally we would say "There isn't a bridge.