For me personally I am happier to remain single until either - by some
divine miracle (I jest not) my ex renounces his current beliefs, becomes born again and also seeks significant marital counselling so that me and the kids can feel safe and that we can be together again as a family. Or that he passes away naturally. In the circumstance of bereavement I would be comfortable to remarry but it would depend on whether it was the Lord's will for me, plus, the husband would have to be a strong believer in Christ.
Now whilst that may work for me, I think that such a stance would be understandably harder if a woman is younger or if you've never had kids.
Whilst it does not specifically address divorcees, 1 Cor 7 is pretty good for giving a little guidance as to how human we all are and also how we can cope with that in terms finding ourselves in the situation of not being married to someone. Although technically we are divorced and not unmarried or widowed a couple of areas in this book stand out in terms of how we conduct ourselves;
1) in verse 2 - if a person runs the risk of being sexually immoral, Paul suggests that it is probably better for a person to marry. I'm not of the school of thought that a divorced person basically has to suck it up and remain single when they 'burn' to the degree that this verse alludes to. We have a forgiving God who we can confidently come to and confess our sins in order to adopt an act which some people would consider a sin, that is, to remarry. If the church fellowship, the potential believing spouse and yourself can see that this option is less worse than being promiscuous, this could be an option.
2) jumping to verse 39 - although this pertains to a widow what stood out for me is the last few words of the verse, "Only in the Lord". So applying this to a divorcee - if a person is in the situation of step one where they cannot remain single (would give way to being biblically sexually immoral) and would look to get re-married, then the husband must be a believer in Christ. As a woman I would seek the guidance of my church leaders in terms of assessing who an appropriate husband could be, on the basis that we have 'messed up before' in terms of choosing a spouse. I would be less inclined to rely on my own judgement of what constituted a good husband and I would seek expert counsel in other believers/Christian Marital organisations.
3) looking at verse 34 - there is a reference to the unmarried woman or the virgin. Basically such women should be focused on 'the things of the Lord' i.e. being constantly in His Word, fellowshiping with other female believers etc. Why? So that she does not get distracted by other factors and she is 'holy both in body and in spirit'. I guess what this looks like in practical terms are those moments day to day when instead of thinking about being single/factors linked to that, our thoughts are turned towards a Bible verse or study that we are chewing over, we are hanging out with friends where we can talk freely about Christ, we are basically occupying our day with all things which in turn removes the focus away from multitude of factors attached to being single, especially after a divorce.
I am sure someone will probably offer something better than my ramblings but this was just my very little tuppence in terms of what came to mind.