Delta is supposedly free (or at least the same for a bike as a regular bag), ie. per the below excerpt.. Some news articles indicate this applies to int'l as well.
Just curious.. why aren't you just going direct to Vienna? I'm guessing you have a train ride planned or somesuch.
Bicycles
Bicycles, non-motorized touring or single seat racing, are allowed as checked baggage on most flights, with the exception of certain Delta Connection® carriers.
Standard baggage allowance and fees based on cabin and travel region apply
Bicycles weighing over 50 lbs. will be charged the applicable excess weight fee
If the outside linear dimensions (length + width + height) exceed 115 linear inches (292 cm) or exceeds 100 lbs, the item will not be accepted
Items in excess of baggage allowance will be subject to additional or overweight baggage fees
A limited liability release form must be signed by the passenger in the case that the bike is not properly packed
If the bicycle is packaged in a hard shell case specifically designed for transporting bicycles, then a limited release form is not required
If the bicycle is packaged in a soft sided travel bag or anything other than a hard shell case, a limited release form will need to be signed