I would second Tom Cotton’s suggestions of Bloomingtona or Blumingtona. Bloomingtonia or Blumingtonia doesn't seem incorrect either. (If you want to completely assimilate the word to Latin phonotactics—which I don't think is necessary—you could simplify the consonant cluster "ngt" to "nt".) One argument I can think of in favor of using "-tonia" is that English speakers already use "Bloomingtonian" as an adjective, like "Bostonian" or "Houstonian". But on the other hand, English is not Latin.
Note: I am still a beginner in Latin so I have no expertise with regard to this; all of this has been a guess based on a list of Latin place-names I found and other Google research. Please take it accordingly.
Medieval Latin: An Introduction and Bibliographical Guide, edited by F.A.C. Mantello and A.G. Rigg, has a chapter titled "Morphology and Syntax" (by A.G. Rigg) that says that the morphology of place names in Medieval Latin was often "arbitrary" and suggests that the commonly-used feminine suffix -ia may have been "originally seen as an adjectival ending agreeing with urbs or prouincia understood (e.g. Cantuaria, 'Canterbury', Abandonia, 'Abingdon')" (p. 84).
I found a large “List of the Latin Names of Places in Great Britain and Ireland” online; I’m not sure of its sourcing (so it might not be reliable) but a few of the names I checked were corroborated by other sources, so I’m tentatively assuming that it is reliable and only lists terms with some kind of attested use, not ones that are entirely questionable suggestions for neologisms.
I haven’t found any rule for whether to use “-tona” or “tonia” in the Latinization of English place names ending in “-ton”. As varro pointed out, “Bostonia” and “Hustonia” are used, but the list I linked to in the previous paragraph seems to have slightly more examples of “-tona” (e.g. "Chingestona" – Kingston and "Cunctona" – Compton). A document I found while Googling lists the additional variants of “-thonia” (found in “Conthonia”, an alternative name for Compton) and “-tuna” (found in “Stoctuna”, a name for Stoughton) (Sussex Archaeological Collections Relating to the History and Antiquities of the County, published by the Sussex Archaeological Society, Vol. XL). While variation between “th” and “t” and “o” and “u” could be attributed merely to the less fixed nature of orthography in past times, I don’t think the variation between “ia” and “a” can be as easily dismissed as purely graphical.
Here is a (not necessarily complete) list of Latin place names I found in the list corresponding to English place-names ending in “-ton”:
-tona/-tuna/-thona:
- Chingestona (Kingston)
- Cunctona (Compton, Sussex)
- Gaidingtona, Gaingtona (Geddington)
- Hunegetona (Honington or Hunnington, Staffordshire)
- Karintona (Catherington, Hants)
- Mucletona (Mickleton)
- Stiuentona (Staunton, Gloucestershire)
- Waldintona (Waldington, Yorks)
- Cleituna (Clayton, Sussex)
- Mealtuna (Malton, Yorks)
- Tornetuna (Thornton, Yorks)
- Ethona (Nuneaton, which was earlier simply “Etone” according to Wikipedia)
-tonia/-tunia/-thonia:
Bramptonia (Brampton)
Glastonia, Gleastonia, Glestonia (Glastonbury)
Rugnitunia, Ruitonia (Ryton-upon-Dunsmoor, Warwickshire)
Wiltonia (Wilton; Wilts)
Conthonia (Compton; not in the list but in the cited book)
Bostonia (Boston; not in the list)
Hustonia (Houston; not in the list).
Note: it may be relevant that the city of "Houston" was named after Sam Houston, whose name might not have been etymologically connected to the "-ton" suffix found in many other English city names. Thus, it seems possible to me that the Latin name "H(o)ustonia" should be compared to names like "Columbia" from the personal name "Columbus".
either -tonia or -tona/-tuna:
- Hamptonia, Hamtona (Southampton; Northampton; Hampton)
- Northamptonia, Northantonia, Northamtuna (Northampton)
-tonium:
Varingtonium (Warrington, Lancashire)
This is weird and I don't know how to explain it, but it doesn't seem to be a typo. Possibly compare "Vasingtonium", listed on Wikipedia "List of Latin names of cities", but called "quite odd" by somebody on the talk page.
-dunum:
- Burgodunum (Burton, Staffordshire)
- Castrodunum (Chesterton, Cambridgeshire)
- Dorpendunum (Orpington, Kent)
- Ellandunum (Allington, near Amesbury, or Wilton, in Wilts)
- Repandunum (Repton)
- Spinodunum (Thornton, Lincolnshire)
- Sturodunum (Stourton, and Stourminster, Dorset)
- Tanodunum, Thenodunum (Taunton, Somerset)
- Venantodunum (Huntingdon)
I don’t know if the use of “-dunum” is due to contamination from names with “-down” and “-don”. Wikipedia says:
Dunum was a Latinized nameplace in ancient Ireland and the name of at least two recorded settlements there, one in the far north, one in the far south. [...] As a word, Dunum is very similar to words for fortifications and measurements, and sometimes used as a suffix or prefix in placenames to note the presence of fortification.
Interestingly, it seems it is thought to be derived from a Celtic word cognate with “town”. It seems to me that “-dunum”, although relatively common as a final element in established Latin place names, would not be a good choice for Latinizing the names of cities or towns that were named in modern times.
In terms of Latinization of the rest of the name:
as varro pointed out, “oo” could be changed to “u” (which I assume would be pronounced as ū /uː/)
The letter-sequence “ngt”, which does not occur in Latin, might also be changed. Although “nct” seems to me the closest equivalent in sound, I don’t know of any examples of "ngt" being Latinized this way, so I wouldn’t recommend it. Instead, simplifying the cluster to “nt” seems to have some precedent, as well as simply retaining it as “ngt”:
-ingt:
- Gaidingtona, Gaingtona (Geddington)
- Varingtonium (Warrington, Lancashire)
-int-:
- Karintona (Catherington, Hants)
- Waldintona (Waldington, Yorks)
I would just ignore the "weird" examples in the list of Godritona (Codrington) and Hunegetona (Honington/Hunnington).
Incidentally, http://geonames.enacademic.com/12172/Bloomington lists "Blumingtona" as one of the names of "Bloomington" in another language, but it doesn't specify which one! Googling it seems to show that it is used in Serbian (example: I Kodi Zeler spreman za NBA : Nakon Viktora Oladipa, i druga zvezda tima iz Blumingtona odlučila se za NBA ligu) and possibly some other Slavic languages, also some Baltic languages such as Latvian (https://lv.wikipedia.org/wiki/Blūmingtona_(Indiāna)).