What is the Catholic Church's view on marry widows, and the Bible's teachings about it? Is it considered a good thing or a bad thing?
St. Paul says it's better for widows (as for virgins, too) to remain unmarried:
1Cor 7:27 Art thou bound to a wife? Seek not to be loosed. Art thou loosed from a wife* [i.e., a widow]? Seek not a wife.
*by either death of the spouse or separation
But he does not prohibit widows from remarrying:
1Cor 7:28 But if thou take a wife, thou hast not sinned.
especially if the widow is young and cannot contain her sexual desires:
1Tim 5:11 But the younger widows avoid. For when they have grown wanton in Christ, they will marry:
1Tim 5:14 I will, therefore, that the younger [wanton widows] should marry, bear children, be mistresses of families, give no occasion to the adversary to speak evil.
Also, St. Paul says candidates for being a bishop must not have ever remarried:
1Tim 3:2 It behoveth therefore a bishop to be blameless, the husband of [no more than] one wife, sober, prudent, of good behaviour, chaste, given to hospitality, a teacher,
cf. the analogous "1Tim 5:9 Let a [female] widow be chosen of no less than threescore  years of age, who hath been the wife of one husband."
Proverbs 5:18 …rejoice with the wife of thy youth
i.e., honor your first wife.
And the holy young widow Judith didn't remarry, but vowed to remain a widow (cf. Judith 16:22).
The Church discourages but does not prohibit second marriages. The marriage ceremony of widows is more somber, the father does not walk his daughter down the aisle, nor does he unveil her.
St. John Chrysostom's On Not Entering a Second Marriage (pp. 223-44) strongly discourages widows from remarrying.