After you say hamotzi, how much time do you have before you must eat some bread? I note that quantities of food are frequently specified (e.g., at least a kazayit-- an olive's worth, etc.). Are times also specified? My research produced no answer.
There are three different issues here.
1) Time difference between saying a blessing over food (not just hamotzi) and eating that food.
2) Quantity of food and time in which it is consumed to need a blessing afterwards (not just bread)
3) Amount of bread over which it is necessary to say the blessing on the ritual washing of hands.
1) The Kitzur Shulchan Oruch 50 (5) says in this extract:
One shouldn't hesitate more than momentarily (note i) between (making) the blessing and eating (the food). Even while chewing, it is forbidden to make any interruptions until one swallows. An interruption by speaking, between the blessing and eating, about matters not related to the food, requires repeating the blessing. However, if he waited in silence, he does not need to go back and (again) bless. Waiting that's required for the eating isn't considered an interruption at all.
Note i) The time it takes to say the words ''Shalom Alecha Rebbi'' (Mishna Berurah 487:4), or according to the Pri Megadim ''Shalom Alecha Rebbi U'Moree.''
2) See the Star K article where it says:
K’zayis Measurement – 1.27 fl. oz. (38 ml) – If one eats a k’zayis of bread, he must recite birchas hamazon. Similarly, if one eats a k’zayis of any other food a brocha acharona must be recited.
An after-brocha is only recited if one eats a k’zayis in the amount of time known as k’dei achilas pras. This means, to recite Birchas hamazon or a bracha acharona one has to have eaten a k’zayis ideally within a two minute span (b’dieved within a four minute span). The same applies to fulfilling various mitzvos (e.g., achilas matzah).
3) From the same Star K article:
When washing before eating bread, one recites the brocha of Al Nitilas Yadayim only if one intends to eat a k’beitzah of bread (= Two k’zayisim, 2.53 fl. oz. (75 ml) ).
This answer only starts the subject. Study more and CYLOR.
Yes there are times involved as well. For example, HaMotzi Richard B. Aiken specifies.
Wash the One-Time Method and say ha’motzi on bread made of the Five Grains (wheat, rye, oats, barley, or spelt), even if you will not eat at least 1.3 fl. oz. (39 ml, or 1/6 cup) within four minutes.
Note: Say the blessing al netilat yadayim on washing hands ONLY if you will eat at least 1.9. fl. oz. (56 ml) of bread within four minutes.
The bracha rishona applies even for a mashehu (any amount). The specification of a particular amount (kazayis) applies only for how much is required in order that one is to say the birkas hamazon. The bracha rishona statement applies to any food item as explained by Rav Shlomo Aviner. As an example
Q: Does one recite a blessing on chewing gum?
A: Yes, since a blessing before eating does not require a minimal amount (Mishnah Berurah 210:1), one benefits from the sweetness, and it reaches one's stomach (Shut Yabia Omer 7:33 #2. Although the book Bikdushato Shel Aharon [Volume 1 p. 162, 186] relates that when the Chafetz Chaim and the Belzer Rebbe - Ha-Rav Aharon Rokeach - met in a Rabbinical conference in Warsaw, the Belzer Rebbe poured the Chafetz Chaim a glass of wine and said: Here, we arrived at the minimal amount. The Chafetz Chaim immediately understood that the Rebbe meant for the blessing preceding the drinking, and was surprised! The Chafetz Chaim said that this is the position of the Kol Bo [brought in the Beit Yosef, Orach Chaim #210], and apologized, saying that if he had known that there are those who follow it, he would have included it in the Mishnah Berurah! Only those who are the most particular, however, follow this ruling).
Since it applies to the smallest amount of food, there is no time requirement in which the eating must take place. A time requirement only exists if there is a minimum amount of food mentioned (as with birkat hamazon or other bracha acharona.)