I recently read (in what I thought was a pretty reputable grammar book) that "regresarse" is not used in Spain, but I had never heard this before. Is it true? If so, why don't Spaniards use it? Is there a history to it? Was it used at one time in Spain, but no longer? Again, if this is true, how is it that the rest of Latin America uses "regresarse" but not Spain?
regresarse I don't think I've ever heard in Spain. But in any case, in Spain, volver is heavily favored over regresar (that's not to say regresar isn't used, because it is, just less often).
One reason as to the difference in reflexivity could be simply that regresar appears to be a relative late-comer to the language. Based on Google's N-grams, we can see that volver is the standard term, but around the 1800s-1850s, regresar(se) starts growing in use [volver/regresar].
Perhaps due to its later entry into the language, regresar adopted an additional transitive meaning in American Spanish ("ella regresó el libro" = "ella devolvió el libro" in Spain), and perhaps by analogy with other verbs that are pronominal when used intransitively, some speakers started using the intransitive form pronominally.
But, do note that for not just Spain, but the majority of the Spanish-speaking world, regresar is considered by default non-reflexive. That, of course, is not to say that you're wrong to use it reflexively (because you're not) but only to ensure that you don't think in American Spanish it's obligatory.
I agree with Guifa. From my own experience (center of Spain), your dictionary is right in saying "regresarse" isn't used in Spain.
RAE seems to agree:
2. intr. Volver al lugar de donde se partió. En Am., u. c. prnl. [= en América, usado como verbo pronominal]
NGLE, for its part, isn't any less laconic in describing this expression:
En varios países americanos, aunque no en todos, se emplean demorarse, enfermarse, regresarse a un lugar, soñarse con algo o alguien y otros verbos pronominales similares a estos, a menudo en alternancia con usos no pronominales:
Hay colombianos que 'triunfan' en Nueva York, otros se regresan con los bolsillos vacíos (Tiempo [Colombia], 1/7/1989).
There is some information as to how it is used, but none about how it got to exist only on one side of the pond or since when.
All I can say regarding the first question is that, just as species start differing progressively when they colonize different habitats with little or no communication, so do languages. As an attempt to answer the second question, here's some additional data from CORDE:
As you can see, all contemporary uses of reflexive "regresarse" are by Latin American writers (6), except for one instance in 1946 by a Spanish author. There are a few hits from Spain around 1800's (2), but that's about it.
Other combinations yield similar results:
Summing up the forms "regresarse" (25) + "se regresó" (14) + "se regresa" (14) + "se regresaron" (8) + "me regresé" (6) + "se regresaba" (4) + "se regresaría" (4) + "me regreso" (4) + "se regrese" (3) + "se había regresado" (2) + "nos regresamos" (2) + "se habían regresado" (1) + "se regresaban" (1) + "se regresan" (1) + "se habría regresado" (1)1, you get:
Again, "regresarse" is far more common in Latin America. It's rare in Spain, but it doesn't seem to me that it was used before more than it is used now. The popularity of the term seems to have increased in Latin America, but not in Spain (or maybe there are more works available now, CORDE doesn't show relative numbers as NGram does), the gap between the two being wider now (1:2 up to 1899 vs 1:5 now, approximately). My conclusion is that, rather than being a construction that fell into disuse in Spain, it was in Latin America where the verb "regresar" took on this new form and grew popular.
1: Other forms not listed here returned 0 hits.