This is a list of every time in the Hebrew Bible that X proposes to Y that A should marry B (X and Y can be the same as A and B.) I am not including the cases where a wife offers her slave as a concubine.
There are 10 proposals of marriage in Tanakh (3 in Genesis, 4 in Samuel, 1 in Kings, 2 in Ruth): To make it known how varied and strange are the ways in which people interact.
The English translations below are by Robert Alter.
ועתה אם ישכם עושים חסד ואמת את אדוני הגידו לי ואם לא הגידו לי ואפנה על ימין או על שמאלThe classic arranged marriage. The bride is off stage. The groom is hundreds of miles away. The marriage is arranged between an agent of the father of the groom and the father and brother of the bride. The bride and groom have never set eyes on each other (this is the only example in this collection where that is true.) Acceptance of the proposal is viewed as a kindness that the bride's relatives are doing for the groom's father.
And so, if you are going to act with steadfast kindness toward my master, tell me, and if not, tell me, that I may turn elsewhere.
ויאהב יעקוב את רחל ויאמר אעבדך שבע שנים ברחל בתך הקטנהMarriage arranged between the groom and the father of the bride.
And Jacob loved Rachel and he said "I will serve you seven years for Rachel your younger daughter."
וידבר חמור אתם לאמור: שכם בני חשקה נפשו בבתכם. תנו נא אותו לו לאשה. ... ויאמר שכם ... ותנן לי את הנערה לאשהProspective groom and his father propose to father and brothers of prospective bride. However, this comes after the groom has raped the bride.
And Hamor spoke with them saying, "Shechem my son, his very self longs for your daughter. Pray give her to him as wife." And Shechem said ... "give me this young woman as wife".
ויאמר שאול אל דוד: הנה בתי הגדולה מרב אתה אתן לך לאשה אך היה לי לבן חיל והלחם מלחמות השםProspective bride's father offers bride to prospective groom. However, Saul's real intention is that David should get killed fighting the Philistines.
And Saul said to David, "Here is my eldest daughter, Merab. Her shall I give you as wife, only be a valiant fellow for me, and fight the battles of the Lord."
ויאמר שאול אל דוד: בשתים תתחתן בי היוםProspective bride's father offers bride to prospective groom. However, Saul's real intention is that David should get killed carrying out the condition.
And Saul said to David, "Through the second one you can be my son-in-law now."
והיטב ד' לאדוני וזכרת לאמתךThe demure wording of this notwithstanding, what it clearly actually means is "When my disgusting husband Nabal is dead, let's get married." ("Disgusting" is not my editorializing; Abigail is quite specific about it.) Thus the (already married) prospective bride is proposing to the groom.
Then the Lord will do well with my lord, and you will remember your servant.
דבר נא אל המלך כי לא ימנעני ממך ... ותאמר לו על אודות הרעה הגדולה הזאת מאחרת אשר עשית לשלחניI am not happy about including this, but it does come within my definition. Tamar says the first quote above when Amnon is raping her; she says the second after he has finished and is throwing her out of his room. It is not at all clear how this could possibly work, since he is her half-brother. The first sentence could be a ruse to get away from him; but the second must mean seriously that, having raped her, he is now obliged to marry her.
"And so speak, pray to the king, for he will not withhold me from you." ... And she said to him, "Don't! this wrong is greater than the other you did me, to send me away now."
ותאמר יותן את אבישג השונמית לאדוניהו אחיך לאשה
And she said, "Let Abishag the Shunamite be given to Adonijah your brother as wife."
[Adonijah] seems to have had a talent for doing the foolish thing with a maximum of foolishness, as though anxious not to be misunderstood.
--- Maurice Samuel, Certain People of the Book
ותאמר אנוכי רות אמתך ופרשת כנפך על אמתך כי גאל אתהRuth is a widow without child, and therefore by the law of levirate marriage, the nearest male relative was obliged to marry her so as to produce an "heir" to her late husband. Ruth is reminding him of this.
And she said, "I am Ruth your servant. May you spread your wing over your servant, for you are a redeeming kinsman."
ומאת רות המואביה אשת המת קנית להקים שם המת על נחלתוBoaz reminds the unnamed nearer relative of his responsibility.
You will also acquire Ruth the Moabite to raise up the name of the dead man on his estate.
There's a lot of violence here. 5 of the 10 episodes involve someone, or many people, being killed, or proposed to be killed.
None of these conform to the model of proposal that was standard, at least in literature, from at least Shakespeare's time until recently: A man asks a woman to marry him; she has the choice to accept or decline. On the other hand, only the first one, of Isaac and Rebecca, conforms to the model of the purely arranged marriage, in which neither bride nor groom is involved and their feelings are not at all consulted.
A propos of the Book of Ruth: the colloquy between Ruth and Naomi at the end of chapter 1 is the only part of Tanakh that passes the Bechdel test