Hi raeberry33,
I’m not sure I would call the Casper mattress a “latex” mattress since it only includes 1.5" of latex along with 1.5" of memory foam and 6.5" of polyfoam which certainly isn’t enough latex to call it a latex mattress or even a latex/polyfoam hybrid mattress.
A box spring has springs inside it that flex under the mattress and there are very few one sided mattresses today that use them as a support system and in many cases they will invalidate a mattress warranty. Most mattresses in the industry today need a steel or wooden bedframe with a foundation that has minimal to no flex (vs a box spring that flexes) or a platform bed which also has little to no flex under the mattress. There are many in the industry that mix up the terminology between box springs and foundations even though they are very different products. You can tell which you have by applying firm pressure and if has noticeable give or flex then it’s probably a box spring and if it’s firm with very little to no flex then it’s probably a foundation.
Any foam mattress with a polyfoam support core such as the Casper mattress will generally do best with a firm, flat, and evenly supportive support surface underneath it that has minimal to no flex under the mattress and for larger sizes with at least one center support beam that has good support to the floor to prevent any sagging in the middle of the mattress. The components (either a bedframe and foundation or a platform bed) need to be strong and durable enough to support the weight of the mattress and the people sleeping on it without some of the parts bending, sagging, shifting, or breaking with extended use. The support surface under the mattress (which may be slats or a steel or wire grid) should have enough surface area to prevent the mattress from sagging through any gaps or spaces in the support surface over time but still allow some airflow under the mattress. If a foundation or bunkie board has a slatted surface then I would suggest that the gaps between any slats are no more than about 5" (with 1 x 3 slats) although less than 4" would be better yet.
A bunkie board on top of a box spring certainly wouldn’t be my first choice and it may still end up sagging over time on top of an older box spring which may have some soft spots and it may not provide a stable support surface for your mattress since it may shift or lead to some side to side sway as well.
If you have a box spring and if I was in your shoes I would replace it with a suitable foundation that was a similar height as your box spring.
Just for reference as well … there are some comments about the Casper mattress along with many of the other “simplified choice” mattresses in post #2 here and the first post in the same topic would be worth reading as well. A forum search on “casper” (you can just click the link) will bring up more comments and feedback about it as well.
Phoenix