I am afraid that if your pic refers to the real location of the substituents (primary side up and secondary down and only one sulfobutyl gropu/CD ring) than the work is very long and complicated. First you need to prepare the mono-6-O-sulfobutylated (SB) CD then crosslink so that each CD is attached not more than 2 other CDs. It is complicated but not impossible. A possible way is that after the preparation of the mono-6-O-sulfobutylated CD - this is not easy, see later -, then 2(3)-O-monoallylation, then protect the hydroxyls (TMS?), epoxydation and deprotection. The epoxy will react practically exclusively with another secondary O under basic conditions perhaps in water (I suspect that the SB-epoxypropyl CD is soluble in water). If you are a fortunate guy, you can find appropriate conditions to get the structure on the pic. However, the preparation of 6-monoSB is a challenging task, because you need to protect all the hydroxyls except one O6 and then this OH can be reacted with butanesultone under basic conditions. Of course, there are some publications dealing with the site selective alkylations (look for e.g. Jindrich et al.) but in those cases the separation of the regional isomers are also difficult, additionally the butanesultone is very reactive and not only substitution but its hydrolysis and other side reactions with the solvent impurities might occur. My opinion that under the described alkylation conditions the O2 substitution would be the most dominant.
If you have the sulfobutylated CD yet (commercially available SBCD), in that case you cannot do anything, because the SB is located practically only on the secondary rim, mainly on O2 and only a few of them is on the primary. In case of cyclodextrins, in the dominant cases of alkylation reactions, the O2 is the most reactive and not the primary one. O3 is usually poorly reactive, due to steric reasons, particularly when the vicinal O2 is substituted (and vice versa, but considerably less extent). In this case you can use epichlorohydrin or diepoxybutane for crosslinking using NaOH or KOH in water. Unfortunately, you will get a complex structure which is surely far from the targeted "linear" polymer and additionally, the crosslinking can occur on all free hydroxyls, not only on the primary ones and you will find dihydroxyalkyl residues, too. But, it is true that by this method you can get a scalable preparation method, with all the drawbacks of the preparation of a randomly substituted derivative.