The defense of the Burnside Bridge was done from a trench, dug into the hill above it. It gave the Confederates an excellent position from which to fire down on the Union troops attempting to cross it. They therefore had no easy chance to actually dismantle the bridge ( which was a big pile of stones that would have taken them quite some time). They were in danger of being flanked by Roman's Rodman's Union troops coming in on them from the south, anyway, so destroying the bridge would have been pointless.

The bridge is still there, and if you walk trails around the creek , you'll see that the creek itself wasn't the big obstacle- it's quite shallow in many spots. The big problem was the very steep slopes overlooking it that were quite hard for Union soldiers to climb, and easy for Confederate skirmishers to defend.

My biggest question after I visited Antietam is why didn't the Union troops just ford the stream? It isn't that big and you could have sent people over in a spread out wave that would make it harder for the sharp shooters to sight in and get everyone.

For one thing, I believe that Lee' general idea was to take the union on in battle and he chose not to destroy that bridge as well a the middle bridge, a bit north of Burnside bridge. If that was the general order then the defenders would have tried to seek permission to change the idea. I am going from memory so someone correct me if they know differently.

Secondly, the bridge is made of stone and would have likely need some sort of demolition to blow it up. You will recall that earlier in the campaign Lee sent one of the independent division ( I believe under John Walker) to blow up one of those C and O canal bridges (i forget the technical name) that span one of the tributaries of the Potomac. I believe this is the one that spans Muddy Branch creek. Walker reported that task was impossible as the bridge was stone and they did not have the type of charge to blow it.

SO its not so easy to blow up stone bridges without some specific types of charge.