The Tigers went down to a 2-0 loss at home to Chelsea on Saturday as goals from Eden Hazard and Fernando Torres took the Blues top of the table.
But Hull boss Bruce is optimistic that some good news on the transfer front will help his side move on from defeat.
Talks are due to begin in the next 24 hours for Jelavic after the clubs agreed a deal on Friday night, with discussions also under way with West Brom regarding fellow striker Long.
"We agreed a fee (for Jelavic) last night. We hope we can persuade him to come here," said Bruce.
"We're trying our best and we'll see what happens.
"We've had a conversation with West Brom about Long's availability at boardroom level but that's as far as that goes at the moment.
"They've appointed a new manager, so I would have thought they would have to have a conversation with him, so we'll see how that develops."
Reflecting on the loss to Chelsea, Bruce admitted that Hull had struggled to maintain their level of performance and picked out Hazard as the main difference between the sides.
"First half we did okay but in the second half we didn't keep the ball well enough" said the Hull manager.
"Hazard was for me the best player on the pitch. He scored a wonder goal and after that it became a very difficult afternoon, it became stretched and open and their top players had more space to show their quality."