The Ibn Ezra on the pasuk writes two noteworthy points:
Bread and a skin of water. Since Hashem told him to listen to all that Sarah said he could not give Hagar anything without Sarah’s permission. Nevertheless, after Sarah’s death he gave the sons of his concubines gifts (25:6).
It is also possible that he gave Hagar gifts that Scripture does not mention. She went and lost her way. Avraham gave her sufficient supplies to reach Beer Sheva had she not become lost.
So according to the Ibn Ezra, the pasuk only lists a very meagre handout from Avraham to show how he was acting on Sarah's instructions, but later after Sarah's death he went out of his way to give them suitable gifts. Alternatively, he did supply them with other things and Hagar was suitably supplied to get to Be'er Sheva but they did not account for her getting lost.
Interestingly, Radak adds that he did not leave her completely in the lurch. Unlike Rashi he says that although the Torah does not mention it, she was given gold and silver so she had the means to gain more supplies when she ran low, and in addition, Avraham reasoned that she might have relatives in the vicinity that she could make her way to.
ויקח לחם וחמת מים, he gave her enough food and water to last for a day or two. She was unable to carry more than that. He also gave her a plentiful supply of water as the distance to Egypt was considerable. On the other hand, she might have had relatives much closer than in Egypt. He gave her also silver and gold so that she could replenish her supplies, although the Torah did not make a specific mention of this.
Finally, I would argue that Hagar did not choose 'an inevitable and horrible death' this was part of her being expelled from the household. Indeed, Rabbeinu Bachya gives a good analysis of the situation:
וישכם אברהם בבוקר ויקח לחם וחמת מים, “Avraham rose early in the morning; he took bread and a skin-bottle of water, etc.” - He should have given Hagar silver and gold and camels to transport both her, Ishmael, and their belongings seeing he had plenty of money to spare. After all, had he not prayed for his son’s welfare in 17:18 saying to G-d: לו ישמעאל יחיה לפניך, “if only Ishmael live (a good life) in Your presence?” However, seeing that Sarah had told him to expel Hagar and her son, and G-d had told him to obey everything that Sarah said to him (verse 12), Avraham complied and expelled them with the minimum of creature comforts plus a survival kit only. This is Ramban's view.
He adds further:
One may view the fact that Avraham provided Hagar with bread and water as an allusion to something that he foresaw concerning the future when his descendants would be oppressed by the Arabs. He foresaw that the Ishmaelites would hate the Jews more than any other nation on earth hated them. Avraham was careful not to deny Hagar and Ishmael the necessities to ensure their survival, something with which Jews provide even their enemies. He modelled himself after Mishlei 25:21 “If your enemy is hungry feed him bread; if he is thirsty, give him water to drink.”
So according to Rabbeinu Bachya, Avraham had to comply with Sarah's request and therefore he gave them the basic necessities to live, possibly realising that Yishmael would give rise to a future enemy of the Jewish people.