I’d say whether she has a right to or not isn’t the point but try to think of it if the situation was reversed. Wouldn’t you want to know? Is there any harm in putting her mind to rest? If she keeps asking and you’ve refused to tell her that may be fueling her concern.
My question wouldn’t be about rights but would be why haven’t you simply just responded? Not responding infers that there’s an issue you’re attempting to gloss over!
Youve got years ahead to coparent. Having a new partner is bound to make the situation a little prickly.
Though camp beds and the like can be appropriate, this should be a short term plan. As the children are entitled to a place of permanent and privacy. Likewise, many parents would deem it inappropriate for their children to be in the same bed or room as the new partner. The ages and genders of the children also has a bearing.
Likewise your children shouldn’t feel like the poor relation in your girlfriends home.