I did search a lot regarding flower delivery options back in 1976 New York, but wasn't able to find anything of value there. But here is what I could find.
The first floral wire service, established by a group of 15 US florists in 1910, was Florists' Telegraph Delivery Service (FTD). The group was formed as a cooperative and was mutually owned by its members. Members exchanged orders via telegraph messages and hence the name 'wire service' was used to identify the order exchange business model. In 1965, with the introduction of international order sending, FTD changed its name to Florists' Transworld Delivery.Source
I visited the FTD website here and other rival websites for flower delivery in US but under their Terms and Conditions for what the representative is supposed to do if : the recipient is unavailable or refuses to accept the order...is unclear. What I could find was this:
Delivered by an FTD® Florist If the recipient is unavailable to
receive the delivery, the florist will either: For residential
deliveries, if the recipient is not available at the time of delivery,
the delivery person may leave the gift in a safe place for the
recipient to retrieve when they return or attempt delivery the next
day. During the holidays deliveries may be made as late as 9p.m. For
business deliveries, if the business is closed or not accepting
deliveries, delivery will be attempted the next business day. During
the holidays deliveries may be made as late as 5p.m.
What we can actually be certain of are these points:
Travis didn't have a telephone in his room. Thus when Betsy (if she has) refused the order, the representative wouldn't have been able to call back Travis and get his address.
We don't see Travis asking for Betsy's address; true but he may have sent it to her office, or he might have got that information from any other fellow taxi drivers. In the last scene, Betsy never tells Travis where to stop; which implies he knew where she lived.
3 From here: We are sure the flowers were for real(unlike many theories floating around that they were hallucinations as was Betsy herself. )
Martin Scorsese says he intended to film this as being like Catholic
Mass—with Travis lighting shoe polish on fire before burning the
flowers, kind of like a priest lighting candles. However, this is a
parody of Mass—instead of being a ceremony of life, it's a ceremony of
death. (Scorsese says he was aiming for the same sense of a Mass-like
ritual in the scene where the gun dealer lays out guns on a bed like
he's preparing an altar).
Which leaves us with the option that the flowers were actually returned at Travis's place.
In a quest to delve deeper into the subject I had a conversation with an FTD representative (which I admit was a bit unorthodox, but I do have screenshots) where I confirmed that there is actually an option of calling them up and adding a "if undelivered please mail to:" address right after you place the order.This being an option now, must have been an option then as well. We are talking about 1975-76 whereas FTD started in 1910.
So here is my idea of what might have happened: Travis, after the theater episode, was unsure of Betsy's interest in him to have further communication. So while placing the order, he also mentions his address as he didn't have a phone of his own. The representative visits Betsy and she refuses to accept the order and thus in case of absence of Travis's home phone number it gets sent to his apartment.