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It is perfectly right for a widow to stay single if she wishes. There is no compulsion in the Bible either to marry or to remain unmarried.
For those who are baptised into Christ, Paul gives the following advice.
NKJV 1 Corinthians 7:8 But I say to the unmarried and to the widows: It is good for them if they remain even as I am; (Paul was unmarried)
9 but if they cannot exercise self-control, let them marry. For it is better to marry than to burn with passion.
The only restriction placed on those who have been baptised into Christ is that if they do marry it should be to someone who is also a baptised believer.
1 Corinthians 7:39 The wife is bound by the law as long as her husband liveth; but if her husband be dead, she is at liberty to be married to whom she will; only in the Lord.
This is so that they will be a help instead of a hindrance in living a life in Christ.
If you want to come to grips with what the Bible really teaches, why not take the free online Bible study course available on our website, www.thisisyourbible.com? This course will give you a background in the major themes of the Bible from Genesis to Revelation. As with everything we offer, there is no cost to you other than your time and effort... You will also have a personal tutor to whom you may pose questions either from the course itself or those questions which come to you as you read the Bible.
I hope this helps.