A menopausal woman is halachically considered mesuleket damim (a woman who no longer sees blood). A mesuleket damim does not need to keep any vesatot. If a mesuleket damim experiences uterine bleeding, she is niddah, and is obligated in all the laws of niddah like any other woman.
Different reasons can be given for Torah commandments, and some might be true to the spirit of Torah and halacha. However, the reason for keeping the laws of niddah, as with any other Torah commandment, is that the Torah obligates us to do so. The obligation applies only to women who enter the niddah status, and in practice does control a couple's marital life to some extent. But the reasons given for keeping these laws do not create a requirement to observe them when a woman no longer becomes niddah. Therefore, pregnant women, menopausal women, and women who are not niddah for any other reason for long stretches of time, are not obligated to separate from their husbands at any time, and there are no constraints on their sexual lives. If you find it is taxing on your relationship to be together all the time, we suggest you speak to your husband and come to some arrangement about times that you both agree to refrain from sexual activity. Both of you would have to be in full agreement in order to implement such an arrangement. Keep in mind that it is not a halachic arrangement, but a personal one.
You are allowed to go to the mikveh with no prior bedikot or days of waiting. Since you are not obligated to immerse, you are not obligated in any preparations for immersion either. If you feel the preparations enhance your experience, you are permitted to prepare as you normally would. Here again, keep in mind that your immersion is for a spiritual purpose alone, and has no practical halachic implications. Reciting a brachah is not permitted in an optional immersion, and reciting it would be a brachah levatalah (reciting a blessing in vain).
It would be best to explain the situation to the mikveh attendant and consult with a local rabbi.