Invite, bid, solicit, court, woo are comparable when they mean to request or encourage a person or a thing to come to one or to fall in with one's plans or desires.
Invite in its ordinary and usual sense implies a courteous request to go somewhere, do something, or give some assistance which it is assumed will be agreeable or at least not disagreeable to the person invited.
In this sense the word usually implies providing an opening for those who otherwise might hesitate to go, or do, or give without such a request. Consequently, in its extended sense invite implies providing an opening by such means as a seductive manner or a challenging statement or policy that serves as an encouragement or temptation to another.
Bid (see also COMMAND ) is increasingly uncommon in the sense of to request the presence of (as at a feast or great occasion), but bid (usually with for), from its sense to offer a price for something up for sale, has developed an extended use in which it means to make an effort to win or attract or an appeal (as for sympathy) and in this use sometimes comes close to invite in conveying the notion of offering a tempting opening for something,
Solicit (see also ASK 2 ) differs from invite in stressing urgency or need rather than courtesy in requesting or encouraging,
Court basically implies an endeavor to win the favor of a person (as by flattery, attentions, or making love). Only in its extended sense does it imply a providing of a favorable opportunity by tempting or encouraging something to come to one or to happen to one,
Woo basically implies amorous courting; consequently, in its extended sense it frequently stresses a drawing to or upon one by allurements, blandishments, and extravagant promises. Occasionally the word is very close to court and scarcely distinguishable from it.