What is maximum time to visit the Netherlands for someone from Bonaire without a Dutch passport?

Bonaire does not have a separate nationality from the Netherlands. As a Dutch national, you can stay for an unlimited time in the Netherlands. You are not under the 90/180 rule for the rest of the Schengen area or other non-Schengen EU countries. Instead, you enjoy freedom of movement under the relevant EU directive.

However, you will not be able to exercise that right without proof of your Dutch nationality. The best way to get that proof is to get a Dutch passport or ID card. You can also get a declaration of Dutch nationality (verklaring van Nederlanderschap) from a Dutch consulate; these are far less costly. (There won't be any Dutch consulates in Bonaire, however, but there are several in the US.) The declaration does not have the weight of a travel document, however, so it may not be very helpful to you in any European country other than the Netherlands.

Also, for the purpose of the Dutch identificatieplicht (identification obligation), the declaration will not suffice, and a Dutch citizen is supposed to use a Dutch document. So even if you intend to remain in the Netherlands for a shorter time, you should get a Dutch passport or ID card. (In practice, it may be unlikely that you'd get in much trouble for failing to do so, however.)

If you travel to Europe with a US passport and without any evidence of your Dutch nationality, you can expect to be treated like a US citizen. If you are deported or fined for overstaying, however, you ought to be able to defend yourself against the punishment by acquiring and presenting evidence of your Dutch nationality.

You should also be careful about the possibility of losing your Dutch nationality by living outside of the Kingdom of the Netherlands and the EU for a period of ten years as a dual citizen. If you are over 28, you may already have lost your Dutch nationality.

The loss of nationality is automatic, but can be prevented by the issue of a Dutch passport, ID card, or declaration of Dutch nationality (when such a document is issued, a new ten-year period begins). It can also be prevented by moving to the kingdom or the EU for a period of at least one year, or by being married to someone who is in certain categories of foreign service.