This is a tough one, especially since there are so many possibilities.
1) There could have been a name change
2) They may have been missed in the 1900 census
3) They may not have been indexed (possible)
4) They may have been indexed with another incorrect surname
5) They may have MOVED out of the area. (if but briefly)
Did you find either one in 1880?
Were either of them in the same area in 1910?
[Was Washington County the home of the wife or her relatives?]
Where did they marry? Alabama? Mississippi? Washington County?
Who were the families / family groups living nearby?
Were there any 'extended family members' living in the district?
Did you find any of the 1910 neighbors in the same area in 1900?
[Was there a mass movement OR did the district boundaries change?]
Could he have been living with 'relatives'?
Could he have been temporarily 'absent' from the family group, perhaps for work?
Were there any other records indicating they were there in 1900?
** Marriages, Tax records, Witnesses for marriages or court proceedings, deaths (was he an informant?)...
Have you found other family members in Alabama (his home state?)
In Arkansas (borders both Bolivar and Washington counties)?
In Louisiana (a stretch, but not that far away)?
When all else fails, there are two old standbys
(1) - the SOUNDEX (Ugh!).
Sounds funny (no pun intended), but I've found more than a few people in the Soundex when I couldn't find them in the online index, using their version of the "Soundex".
(2) - reading the census Page by Page (double Ugh!)
Of course, it would be good to have an IDEA of where to start - in this case Washington County. In addition, it may be better to begin your search in the same neighborhood where he was found in 1910, if possible. Then, spread out from there.
Cities of Washington County, MS:
Think how your ancestors would have perceived the area (history?).
If they didn't own the land, did they work 'for shares'? If not, did they work in a particular industry? Farm land may have had rental agreements, or (better yet) Deeds.
Everyone needed the basics - a way to make a living and feed the family. Sometimes it meant moving in with someone to share living expenses. Other times, it meant moving away to find suitable land / employment. You may or may not have been able to bring the family along right away.
But if ONE family had to move, chances are others did as well. The good news is "they were not alone".
It looks like this is not a hugh wall - and it is not preventing you from finding the family in prior census records (am I correct?).
Regardless, I will continue to search for ways through this wall if you will post a little more about where you are with this research - tell us a little more about the family group, their marriage, information you have verified so far, research methods you have tried, and possibilities you have eliminated.