I know many frum people wear tzitzis to bed, but a while ago a fellow told me that you should wear the tzitzis that you're going to wear the next day, because of an obligation to wear the same set for 24 hours or something like that. I wonder where it says this (if it does). Also, if you have tzitzis you wear specifically for bed (because they often get tangled or knotted etc.), can you wear these and put on a daytime one in the morning before the bracha?
I have never heard of a need to wear the same pair of tzizit for 24 hours. The assumption lends itself to a lot of questions and suffice it to say that the question would be enhanced if you can ask this bachor to provide sources for his statement.
As to your question if you can wear a pair of tzizit specifically for bed and change in the morning before the bracha this is actually preferable:
.... many are careful to wear tzitzit even during the night, and even while sleeping.
There are several reasons for this practice: a) As mentioned above, according to certain opinions, one can fulfill the mitzvah of tzitzit during the night if wearing a designated day garment. b) If waking up after daylight, one will have fulfilled the mitzvah of tzitzit during the morning hours which have elapsed before his wakening. c) According to kabbalah, tzitzit afford a measure of protection to its wearer even after dark.
If one wears tzitzit while sleeping, it is preferable to have "night tzitzit." Otherwise, if one wears the same pair of tzitzit night and day, reciting the blessing on the tzitzit in the morning is problematic, for a new mitzvah is not being performed—it is merely a continuation of the mitzvah from the day beforehand. However, when putting on a different pair of tzitzit in the morning there is no problem with saying the blessing on the new pair—new mitzvah.
As far as I know, the preferable way to do this is to put on a fresh pair of Tzitzis in the morning, so that the Bracha can be said without question, and then sleep in that same pair the following night, changing it in the morning.
This avoids any problems of the Tzitzis being dedicated to the night time, as well as any issues with saying a Bracha on them in the morning.
I heard this from a Rabbi over 20 years ago.
Menachem Posner's comment at eramm's link seems to say the same thing.
So although I have never heard of some obligation to wear the same pair for 24 hours, it is possible this is where the idea comes from: Wear the same pair at night, as the previous day.