This issue is the responsibility of the Scottish Parliament. This Private Members’ Bill, if passed into law, would not apply in Scotland.
The Scottish Government launched a consultation on the future of civil partnerships in Scotland. The Scottish Government is not persuaded that opposite sex civil partnership should be introduced in Scotland, as there is evidence to suggest that demand would be low, and that there would be disproportionate costs associated with introducing the measure. Moreover, the most recent statistics on the number of marriages and civil partnerships in Scotland shows the number of civil partnerships being entered into is continuing to fall, suggesting that where marriage is an option – which now it is for both same-sex and opposite-sex couples in Scotland – couples prefer that form of recognition.
However, there are legally-recognised alternatives to marriage. Many of the arguments for opposite-sex civil partnership seem to be based on perceptions that, for example, marriage is a religious institution. However, it is perfectly possible to have a civil marriage ceremony, if the couple so wish. In Scotland, humanist marriages have also been afforded legal recognition as of 2005. And finally, Scots Law provides some rights already for cohabitants.
Many of these options do not exist in England & Wales, so I can appreciate the motivation behind the Private Members’ Bill which you mention. However, as you may be aware, the SNP has a long-standing position of not voting on matters that only affect England. I hope that the above information reassures you that opposite-sex couples in Scotland have a good range of options in terms of seeking legal recognition of their relationship.